chemical hazards and noise measure

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Unit IV Scholarly Activity

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Instructions

The sampling results for the chemical hazards you tested for Acme Automotive Parts (AAP) are listed in the following table. The volumes that are listed are what you provided to the laboratory.

960 L (8-hour)

5 µg

48 L (8-hour)

Hazard	Analytical Result	Volume (Time)
Manganese Fume		5 µg	30 L (15-minute)
Copper Fume	1 40 µg		960 L (8-hour)
Lead Fume	40 µg
1,2,4 trimethylbenzene			48 L (8-hour)
Toluene	125 µg
Xylene	20 µg
Metal Working Fluids	500 µg	720 L (8-hour)

Part I: For each of the chemical hazards complete the following:

· Calculate the exposure concentration in mg/m3 for the aerosols.

· Calculate the exposure in parts per million (ppm) for the vapors.

· Discuss where you think errors might have been introduced into the results.

Part II: The results for the noise sampling in the following table were recorded from your noise dosimeters. All the samples were collected for the full shift using 90 decibels on the A scale (dBA) as the criterion level and a 5 decibels (dB) exchange rate.

12 hours

8 hours

Location	Shift Length	Result
Shipping/Receiving			8 hours	78.3 dBA (Lavg)
Hydraulic Press					12 hours	93.0 dBA (Lavg)
Metal Working Line	84 dBA (Lavg)
Robotic Welding	80.5 dBA (Lavg)
Hand Welding	81.3 dBA (Lavg)
Paint Booth	79.5 dBA (Lavg)
QA/QC Laboratory	70.0 dBA (Lavg)
Final Inspection	73.5 dBA (Lavg)

Answer the following for each of the locations listed above:

· Convert the results from dBA to percent.

Make sure you show all your work for calculations.

Your assignment must be a minimum of two pages in length, not including title or reference pages. Your assignment must use at least two references. One must be gathered from the CSU Online Library; the other may be your textbook. All references and in-text citations must be formatted according to APA standards.

Resources

The following resource(s) may help you with this assignment.

Citation Guide

CSU Online Library Research Guide

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After reading this chapter, you should be able to:

1. Describe how sound waves are produced, how they propagate,

how fast they travel through air, and how they change with
distance

2. Dene frequency, period, amplitude, starting phase, and wave-
length; interpret time-domain waveforms of pure tones with
different frequencies, amplitudes, and starting phases.

3. Dene how intensity and pressure are related to each other;
specify the minimum reference levels for intensity and pres-
sure; specify the range of audibility for intensity (in watts/m2)
and pressure (in µPa).

4. Understand why and how to use decibels to quantify intensity
and pressure; describe the range of audibility of intensity and
pressure using decibels; dene dB IL and dB SPL; describe the
threshold of audibility across frequency.

5. Perform simple decibel calculations to compare the intensity
and/or pressure of two sounds.

6. Explain the inverse square law and calculate how intensity or
pressure changes with changes in distance.

7. Understand how to combine the outputs of two sounds and
the resulting dB IL and dB SPL.

8. Describe periodic and aperiodic complex vibrations; interpret
time-domain and spectral graphs of complex vibrations;
describe the importance of Fourier analyses.

9. Describe the basic acoustic characteristics of speech and un-
derstand how to read spectrograms.

10. Understand how ltering can be used to shape the spectrum of
noise; recognize commonly used lter shapes.

11. Explain what is meant by resonance; calculate resonance
frequencies for simple tubes of varying length (open at both
ends or only at one end); know the difference between a half-
wave resonator and quarter-wave resonator.

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AN: 1885529 ; Kramer, Steven J., Brown, David K., Jerger, James, Mueller, H. Gustav.; Audiology : Science to Practice
Account: s3921192.main.eds

AUDIOLOGY: SCIENCE TO PRACTICE

We live in a world of sounds, some of which are
meaningful and some of which are just part of
our noisy environment. We often take for granted
the remarkable ability of the auditory system to
extract meaningful sounds from the less mean-
ingful so that we can sense danger, localize the
source of a sound, communicate, learn, and even
be entertained. Even when asleep we learn to
tune out familiar sounds, but may wake up at an
unfamiliar sound. At a noisy party, you can focus
on a conversation with one person while ignor-
ing the background conversations, but readily
become aware when someone calls your name
from across the room or your favorite song be-
gins. When you listen to an orchestra or band you
may find yourself listening to the whole song or
picking out the various instruments. Our ability to
hear in our everyday world requires the auditory
system to process complex sounds from our envi-
ronment. The process of hearing involves the gen-
eration of sounds, their travels and interactions
within the environment, physiological processing
by the ear, neural processing in the nervous sys-
tem, and psychological/cognitive processing by
the brain. The sounds we hear have basic physi-
cal properties that are processed by the auditory
system into meaningful information.

Acoustics is the study of the physical prop-
erties of sounds in the environment, how they
travel through air, and how they are affected
by objects in their environment. As you will
see in this chapter, any simple vibration can be
uniquely described by its frequency, amplitude,
and starting phase. Complex vibrations can be
described as combinations of simple vibrations.
However, not all sounds generated in the envi-
ronment are audible and the audible range may
be different across species; for example, dogs
and cats are more responsive to higher pitched
sounds than are humans. The human ear is ca-
pable of hearing a wide range of frequencies
over an extensive range of amplitudes. But how

does frequency relate to our perception of pitch?
How does amplitude relate to our perception
of loudness? How do we compare the loudness
of sounds across frequencies? How do we use
our two ears to localize the source of sounds?
These types of questions come under the area of
psychoacoustics, which is the study of how we
perceive sound. The psychoacoustic aspects of
sound covered in this chapter include some basic
perceptions of pitch, loudness, temporal integra-
tion, and localization. After reading this chapter,
perhaps you will be able to answer the age-old
philosophical question that goes something like,
“If a tree falls in the woods and there are no
living creatures around, does it make a sound?”

The definitions and terminology reviewed
in this chapter are necessary to be able to bet-
ter understand topics that are covered in the fol-
lowing chapters, including the physiology of the
auditory system, the clinical procedures used to
evaluate hearing loss, and the function of hear-
ing aids. A thorough understanding of acoustics
requires knowledge of some mathematical con-
cepts and formulas; however, in this introductory
text, only the basic concepts are presented and
every attempt is made to keep the mathematics to
a minimum. The interested reader is referred to
other textbooks (Gelfand, 2009; Mullin, Gerace,
Mestre, & Velleman, 2003; Speaks, 2017; Villchur,
2000) for a more thorough treatment of acoustics
and psychoacoustics.

SIMPLE VIBRATIONS
AND SOUND TRANSMISSION

Sounds are produced because of an object being
set into vibration. Some familiar examples in-
clude vibrations of tuning forks, guitar strings,
other musical instruments, stereo speakers, en-
gines, thunder, and the vocal cords while speak-
ing. Almost any object can be made to vibrate,

12. Discuss and interpret graphs related to the psychoacoustic
(perceptual) properties of loudness, pitch, temporal integration,
and localization.

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3. PRoPERTIES oF SoUnD 21

but some objects vibrate more easily than other
objects depending on their mass and elasticity.
Although most sounds in our environment are
complex vibrations, we begin by looking at very
simple vibrations called pure tones. Pure tones
are used by audiologists as part of the basic
hearing evaluation. In addition, an understand-
ing of pure tones is useful because all complex
vibrations can be described as combinations of
different pure tones, which was mathematically
proven by a man named Fourier. Today, we have
electronic instruments that can perform fast Fou-
rier transforms (FFTs) to determine the different
pure tones that comprise any complex vibration.

The vibrating sound source sets up sound
waves that travel, called propagation ( propa-
gate), through some elastic medium, such as air,
water, and most solids. Propagation of sound
through air occurs because of the back and
forth movement of air molecules around their
position of equilibrium in response to the back
and forth vibration of an object. The air mole-
cules closest to the vibrating object move back
and forth first. Because of the inertial and elastic
properties of the air molecules, the air molecules
only move within a localized region, but as they
push against adjacent air molecules the process
repeats itself, which causes the pressure varia-
tions to propagate through the medium. When
the vibrating object moves outward, the air mol-
ecules are pushed together causing an increase
in the density of air molecules (more molecules
per volume), called condensation, and this cor-
responds to an increase in sound pressure. When
the vibrating object moves in the opposite direc-
tion, there is a decrease in the density of air mol-
ecules, called rarefaction, and this corresponds
to a decrease in sound pressure. Figure 3–1 il-
lustrates how these increases and decreases in
the density of air molecules occur in response to
a simple vibrating object such as a tuning fork.
When the vibration repeats itself over and over,
as depicted in Figure 3–1, there are continuing
cycles of condensation and rarefaction that pro-
duce a continuous sound that can be measured
at different points in the surrounding area. In
Figure 3–1, you can see the areas in which the
air molecules are more densely packed (conden-
sations) and where the air molecules are less
densely packed (rarefactions). The condensa-

tions and rarefactions reflect a repetitive pattern
of increasing and decreasing air pressure. For un-
obstructed sound waves in air, the air molecules
move outward in a spherical direction and the
actual size of the air pressure peak (amplitude)
diminishes with distance because of friction, as
well as because the pressure is being radiated in
an increasing spherical pattern. At some distance
from the source, the pressure will no longer be
measurable because the energy is spread out
over a large enough spherical area. The actual

Tuning Fork

rarefac on

condensa on

rarefac on

condensa on

FIGURE 3–1. A and B. Illustration showing pro p-
agation of air molecules to a vibrating sound source.
A. Tuning fork vibration producing alternating areas
of increased density of air molecules (condensation)
and decreased density of air molecules (rarefaction)
that are propagated across the air from its source.
B. Sound waves as they propagated spherically away
from the sound source with alternating condensation
and rarefaction phases. As the distance from the
sound source increases, the force is distributed over
a wider area.

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AUDIOLOGY: SCIENCE TO PRACTICE22

amplitude of a sound at any point in space ob-
viously depends on the original intensity level
of the sound, that is, louder sounds will travel
greater distances than softer sounds.

Sound propagation can also be influenced by
how the waves are reflected or interfered with by
objects or walls. Much of our real-world listening
situations are in closed environments, whereby
much of the sound energy does not penetrate
the walls but instead bounces off or is absorbed
by the walls. The angle at which a sound will
bounce off a wall is similar to a ball bouncing
off a wall. The angle of reflection will depend on
the angle of incidence relative to the perpendic-
ular. This becomes even more complicated when
the encountered object is curved (convex or con-
cave), or in a room with four walls, where the
sound may bounce back and forth among the
walls. How sound waves might interact with an
object in its environment is also important. Some
sounds will bounce off an object, whereas other
sounds easily go around the object, and depends
primarily on the sound’s wavelength (see section
on wavelength). As you will learn in the follow-
ing sections, there are also areas in which the con-
densation phase of a wave meets up with another
wave’s rarefaction phase, resulting in wave can-
cellation (where no sound is present). In addition,
materials have certain absorption characteristics
that come into play in determining how sounds
act in the real world. Understanding acoustics
in these types of environments is especially im-
portant when designing theater or music venues
(something acoustic engineers are trained to do,
but it is well beyond the scope of this textbook).

Another characteristic of sound waves is
the speed or velocity with which they are prop-
agated through the medium. Sound travels faster
in water and most solids than it does in air.
The speed of sound in air is about 343 m/s or
1126 feet/s,1 which is much slower than the
186,282 miles per second that light travels. You
probably use this knowledge, maybe unknow-

1 The speed of sound in air is dependent upon both the
temperature and the density. The value used in this
textbook is an approximation for 68°F. The speed of
sound in air slows down as temperature decreases, for
example, it is about 341 m/s or 1086 feet/s at 32°F.

ingly, when you estimate how many miles away
you are from a storm by counting the seconds be-
tween seeing the lightning (seen instantaneously)
and hearing the thunder (heard later). Your esti-
mate of how far away the storm is will be more
accurate if you divide the number of counted sec-
onds by five to take into account that the speed
of sound is about one-fifth of a mile per second.

When the increases and decreases in pres-
sure occur in the direction of the vibrating ob-
ject, as for sound waves, the sound is called a
longitudinal wave. The process of localized back
and forth movement of air molecules results in
the propagation of a longitudinal sound wave
through the air, more precisely in a spherical pat-
tern. When this sound wave reaches the ear, the
corresponding condensations and rarefactions
in air pressure cause the tympanic membrane to
move in and out, thus beginning the process of
hearing. You will see in the next chapter how
vibrations are received by the ear and how the
ear transforms the incoming vibrations into audi-
tory information. Before that, however, we need
to turn our attention to understanding the basic
physical parameters of sound, frequency, ampli-
tude, and starting phase.

FREQUENCY

Pure tones are characterized by regular repeti-
tive movements. Imagine holding a pencil in your
hand and moving it up and down on a piece of
paper at a consistent height and speed. As you
are moving your hand up and down, begin to
move the paper from right to left; you should see
a pattern that looks something like those shown
in Figure 3–2. The actual separation of the peaks
that are produced will depend on the speed at
which you move the paper (the slower the paper,
the closer the peaks). To be able to quantify the
pattern of vibratory movement, the motion is
displayed as a function of time along the x-axis.
The y -axis represents a measure of magnitude or
amplitude of the vibrations (e.g., how far up and
down you moved your hand). When the pattern
of movement is displayed with amplitude as a
function of time, it is called a time-domain wave-
form or simply a waveform.

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3. PRoPERTIES oF SoUnD 23

A cycle of vibration describes the pattern
of movement as the object goes through its full
range of motion one time. In other words, one
cycle represents the movement of an object from
its starting point to its maximum peak, then to
its negative peak, then back to its starting point.
Figure 3–3 shows one cycle of a pure tone.

Most vibrations repeat themselves; therefore,
pure tones are usually described by how many
cycles occur in 1 second (s), called frequency of
vibration. However, instead of using cycles per
second as the unit of measure for frequency, the
term hertz (Hz) is used to mean the same thing.
For example, a vibration that repeats itself 100
cycles in 1 s is called a 100 Hz pure tone. Con-
versely, a 100 Hz pure tone would complete 100

cycles in 1 s. An 8000 Hz pure tone completes
8000 cycles in 1 second. The frequency range of
audibility for humans is from 20 to 20,000 Hz.

Figure 3–4 shows some examples of differ-
ent frequencies as they would appear on paper
when graphed with a 1 s time scale. As you can
notice, it is difficult to visually count the number
of cycles as the frequency increases, and count-
ing would be extremely difficult for much of the
audible frequency range if graphed using a 1 s
time scale. However, another way to graphically
represent the different frequencies of pure tones
is to change the time scale along the x-axis. In
other words, only a few cycles (or even a single
cycle) are plotted over a specified time scale. The
actual frequency is calculated from knowing how
long it takes to complete one cycle, called the pe-
riod of the vibration. Figure 3–5 shows some ex-
amples of how the period is related to frequency.
In Figure 3–5A, you can see that the time it takes
to complete the one cycle is equal to 0.01 s (one
hundredth of a second), which means it would be
able to complete 100 cycles in 1.0 s (100 Hz). In
Figure 3–5B, the time it takes to complete the one
cycle is 0.001 s, which means this vibration would
be able to complete 1000 cycles in 1 s (1000 Hz).
In Figure 3–5C, the time it takes to complete the

Time (arbitrar

)

A
m

pl
itu

de
(

ar
bi

tr
ar

Time (arbitrary)

A
m
pl
itu
de
(
ar
bi
tr
ar
y)

FIGURE 3–2. A and B. Representations of two dif-
ferent pure-tone vibration patterns as a function of
time in arbitrary units. The vibration in (A) is slower
than the vibration in (B) even though the time scales
are equal.

FIGURE 3–3. Time domain waveform showing one
cycle of vibration. The vibration moves from its start-
ing point to its maximum peak (amplitude), then to
its negative peak, then back to its starting point as a
function of time.

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AUDIOLOGY: SCIENCE TO PRACTICE24

one cycle is 0.0001 s, which means this vibration
would be able to complete 10,000 cycles in 1 s
(10,000 Hz). You can see that there is a reciprocal
trade-off between the period and the frequency.
The following equation shows how you can cal-
culate the period (T ) if you know the frequency,

or how you can calculate the frequency ( f ) if you
know the period:

T (in seconds) = 1/f (in hertz)

f (in hertz) = 1/T (in seconds)

This inverse relation means that as the frequency
increases, the period decreases and vice versa.
It is also important to keep in mind that when
frequency is described in hertz (Hz), the period
would be calculated as seconds. However, other

Time (seconds)

0.0 0.2 0.4 0.6 0.8

1.0

A
m
pl
itu
de
(
ar
bi
tr
ar
y)
Time (seconds)
0.0 0.2 0.4 0.6 0.8 1.0
A
m
pl
itu
de
(
ar
bi
tr
ar
y)
Time (seconds)
0.0 0.2 0.4 0.6 0.8 1.0
A
m
pl
itu
de
(
ar
bi
tr
ar
y)

A
B

FIGURE 3–4. A–C. Examples of three different fre-
quencies as they would appear over a 1.0 s time scale.
The number of cycles per second determines the fre-
quency of vibration. The more cycles per second, the
higher the frequency.

seconds
milliseconds

.010000.007500.005000.0025000
10.007.505.002.500

A
m
pl
itu
de
(
ar
bi
tr
ar
y)
seconds
milliseconds

.001000.000750.000500.0002500
1.000.750.500.2

A
m
pl
itu
de
(
ar
bi
tr
ar
y)
seconds
milliseconds

.000100.000075.000050.0000250
0.1000.0750.0500.0250

A
m
pl
itu
de
(
ar
bi
tr
ar
y)

A
B
C

FIGURE 3–5. A–C. one cycle of vibration for three
different frequencies, each plotted with a different
time scale. The time it takes to complete one cycle
is the period. In (A) the period is equal to 0.01 s (one-
hundredth of a second), which means the vibrating
object would be able to complete 100 cycles in 1.0 s
(100 Hz). In (B), the period is 0.001 s, which means
this vibration would be able to complete 1000 cycles
in 1 s (1000 Hz). In (C) the period is equal to .0001 s,
which means this vibration would be able to complete
10,000 cycles in 1 s (10,000 Hz).

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3. PRoPERTIES oF SoUnD 25

units are often used, and you must be sure to
use the appropriate units when making conver-
sions between frequency and period. For exam-
ple, frequency is often measured in units of kilo-
hertz (kHz) (kilo means 1000), such that 1 kHz =
1000 Hz, 2 kHz = 2000 Hz, and so forth. In ad-
dition, the period of pure tones is often mea-
sured in units of milliseconds (ms) (milli means
1/1000), such that 1 ms = .001 s, 2 ms = .002 s,
and so forth. Table 3–1 shows the relation be-
tween period and frequency for pure tones com-
monly used in studies of hearing and hearing
tests. As the pattern in Table 3–1 shows, for each
doubling of frequency, the period decreases by
half; and for each halving of frequency, the pe-
riod doubles. To help understand the relations
in Table 3–1, try covering one column at a time
and see if you can fill in the correct information
by using the information in the other columns.
Fortunately, there is an electronic instrument, a
frequency counter, that can be used to measure
the frequency of pure tones.

PHASE

Pure tones are also called sine waves or sinu-
soids because of their relationship to a sine func-
tion. As illustrated in Figure 3–6, one cycle of
a pure tone is the equivalent of making a full
revolution around a circle, where each point on
the waveform can be described by its sine func-
tion relative to its phase angle (sin θ). You can
think of a vibration starting at the object’s resting
(non-vibratory) state, designated as zero degrees
[sin (0) = 0], then reaching its maximum positive

peak at 90° [sin (90°) = 1)], returning to its initial
point at 180° [sin (180°) = 0], reaching its max-
imum negative peak at 270° [sin (270°) = −1],
and finally returning to its starting point at 360°
[sin (360°) = 0]. As Figure 3–6 shows, any point
on the waveform can be found using the rela-
tionship sin θ = x/r. For example, if θ = 45º, then:

x = r [sin (45º)]

x = r (0.707)

Starting phase refers to the point along the
waveform’s cycle where the vibration begins,
and is expressed in degrees relative to the angle
around the circle. In other words, does the vi-
bration first begin to move in the condensation
direction or the rarefaction direction, and from
what point does it begin? The waveforms shown
in the previous figures have been plotted with a
0° starting phase, which means that the vibration
begins from its equilibrium point and first moves
toward the condensation peak, conventionally
plotted as positive amplitude in the upward di-
rection. Waveforms can begin at any point in
their range of movement, and initially move to-
ward the condensation peak or rarefaction peak.
Figure 3–7 shows an example of a sinusoid with
a 180° starting phase. In this case, the vibration

TABLE 3–1. Relationship between Frequency and
Period (in Seconds and Milliseconds) for Commonly
Used Frequenci

Frequency (Hz) Period (s) Period (ms)

250 0.004

4.0

500 0.002

2.0

1000 0.001 1.0

2000 0.0005 0.5

4000 0.00025 0.25

8000 0.000125 0.125

FIGURE 3–6. The projection of one cycle of a pure
tone as it would appear relative to its position on a
circle. one cycle of a waveform is the equivalent of
making a full revolution around a circle. For example,
the peak positive (condensation) point is equivalent
to a 90º angle relative to the beginning point. The
peak negative (rarefaction) point is equivalent to 270º
(three-quarters around the circle). Equilibrium points
occur at 0º, 180º, and 360º. These simple vibrations
are often called sine waves because each point on the
waveform can be expressed as a sine function (sin θ =
x/r) relative to its angle (θ).

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AUDIOLOGY: SCIENCE TO PRACTICE26

begins at its equilibrium point, but first moves
toward the rarefaction peak and continues its full
cycle until it ends up back in equilibrium at the
180° starting point. Figure 3–8 shows an exam-
ple of two waveforms with the same frequency,
but with different starting phases, one with a 90°
starting phase and one with a 270° starting phase.
A 90° starting phase means that the vibration be-
gins from its point of maximum condensation,
moves to its equilibrium point (amplitude = 0),
continues to its point of maximum rarefaction,
back to its equilibrium point, and finally ends
its cycle at the point of maximum condensation
(where it began). A 270° starting phase means
that the vibration begins from its point of maxi-
mum rarefaction, moves to its equilibrium point,
continues to its point of maximum condensation,
back to its equilibrium point, and finally ends its
cycle back at the point of maximum rarefaction
(where it began).

Our ears are not sensitive, per se, to the start-
ing phase; a pure tone with a starting phase of
0° will sound the same as with a starting phase
of 270°. However, starting phase, or phase in
general, has more relevance when two or more
sounds interact with each other acoustically, be-
fore reaching the ear. For the example in Fig-
ure 3–8, can you predict what the resulting sound
would be? If you answered, “no sound,” you

would be correct, since in this example the two
waveforms would cancel each other out due to
the condensation in one wave offset by the same
amount of rarefaction in the other wave. Fig-
ure 3–9 again demonstrates this phase inter-
action with two relatively simple examples, in
which two tones of the same frequency, but with
opposite starting phases, are combined. For the
two examples in Figure 3–9, the two tones are
180° out-of-phase with each other. Notice that
the 180° out-of-phase relation between these (or
any) two pure tones of the same frequency is
maintained at all points in the waveform. Again,
for these examples there would be no resulting
sound pressure (and no sound) generated be-
cause each condensation point would be can-
celled out by an equal rarefaction point, and the
net displacement would be zero. Figure 3–10
shows two examples of what happens when you
combine two tones of the same frequency that
are not 180° out of phase. In these examples, the
phase relations of the two waves are more com-
plicated and can produce places of cancellation
when the points are in opposite phase directions
or produce places of enhancement when the
points are in the same phase direction. The in-
teraction of two pure tones becomes even more
complicated when they are of different frequen-
cies as shown in Figure 3–11. In these relatively

Time (arbitrary)
A
m
pl
itu
de
(
ar
bi
tr
ar
y)

180º start phase

FIGURE 3–7. one cycle of a pure tone beginning at
180º starting phase. In this example, the movement
begins in the direction of the rarefaction phase of
vibration.

Time (arbitrary)
A
m
pl
itu
de
(
ar
bi
tr
ar
y)

90º start phase

270º start phase

FIGURE 3–8. Two pure tones at the same frequency,
but with different starting phases. In this example,
the two waveforms are 180º out of phase with each
other.

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3. PRoPERTIES oF SoUnD 27

simple examples, the pairs of pure tones have the
same 0° starting phase, but because they are of
different frequencies the phase relation between
the two pure tones changes at different points
in time. The phase of an individual pure tone or

resultant combination of pure tones at any point
in time is called the instantaneous phase. When
a sound is made up of more than one pure tone,
the resultant waveform no longer matches the
pattern of a sine wave (i.e., simple wave) and is
considered to be a complex vibration. As more
pure tones are combined, with or without the
same starting phases, the less the waveform re-
sembles a sinusoid (complex vibrations are dis-
cussed more in a later section of the chapter).

AMPLITUDE

Amplitude is a general term to describe the mag-
nitude of a sound; the larger the magnitude, the
higher the amplitude. Figure 3–12 shows the
waveforms of pure tones with the same frequency
and starting phase, but with different maximum
amplitudes along the y -axis.2 For a vibrating

2 One can describe any sinusoidal vibration by the fol-
lowing equation: a(t) = A sin (2π ft + θ) where a(t) is the
instantaneous amplitude as a function of time, A is the
maximum amplitude, 2πf (also called angular velocity, ω)
is a measure of revolutions around a circle, and θ is the
starting phase in radians.

A
m
pl
itu
de
(
ar
bi
tr
ar
y)
Time (arbitrary)
A
m
pl
itu
de
(
ar
bi
tr
ar
y)

Time (arbitrary)

450 start phase

900 start phase

250 start phase

2700 start phase

Sum 450 and 900 waves Sum 250 and 2700 waves

A B

FIGURE 3–10. A and B. Examples of how two pure
tones of the same frequency, but with different start-
ing phases, can result in different patterns of vibra-
tion resulting from the summation of the two original
waveforms.

A
m
pl
itu
de
(
ar
bi
tr
ar
y)
Time (arbitrary)
A
m
pl
itu
de
(
ar
bi
tr
ar
y)

Time (arbitrary)
A B

FIGURE 3–9. A and B. An illustration of how two
pure tones of the same frequency, but 180º out of
phase to each other, will cancel each other out. In (A) the
solid curve represents a sound with a 0º starting phase
and the dashed curve represents a sound with a 180º
starting phase. In (B) the solid curve represents a sound
with a 270º starting phase and the dashed curve re p-
resents a sound with a 90º starting phase.

A
m
pl
itu
de
(
ar
bi
tr
ar
y)
Time (arbitrary)
A
m
pl
itu
de
(
ar
bi
tr
ar
y)
Time (arbitrary)
A B

FIGURE 3–11. A and B. Examples of how two pure
tones with different frequencies, but with the same
starting phase, combine to give different patterns of
vibration resulting from the summation of the two orig-
inal waveforms.

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AUDIOLOGY: SCIENCE TO PRACTICE28

object, maximum amplitude is related to how
far the object moves back and forth. For sounds
propagated through air, larger amplitudes create
greater amounts of condensation and rarefaction
of the air molecules. The amplitude scale along
the y-axis is often expressed in units of displace-
ment, intensity, or pressure.

Amplitudes vary across the waveform; there-
fore, we need to have a way to specify the over-
all amplitude of a waveform. Because pure tones
have equal positive and negative amplitudes, tak-
ing an average of the amplitudes at all points
would result in zero amplitude and would not
be useful at all. Instead, it is common to use the
root-mean-square (RMS) amplitude (Arms) to ob-
tain an average amplitude for the waveform. As
shown in Figure 3–13, to obtain the RMS ampli-
tude: (1) square each of the instantaneous ampli-
tudes to eliminate any negative values, (2) aver-
age the squared values, and (3) take the square
root of the average. The RMS amplitude is used
in many applications and, fortunately, there are
electronic instruments available that directly mea-
sure the RMS amplitudes of pure tones and other
sounds. Figure 3–14 illustrates two other ways to
describe the overall amplitude of pure tones. One
way is to take the amplitude change between the
positive peak and the negative peak, called peak-
to-peak amplitude (Ap-p). Another way is to mea-
sure the amplitude from baseline (zero) to one of
the peaks, called peak amplitude (Ap). The RMS

amplitude for a pure tone is equal to 0.707 times
the peak amplitude; however, this is not the case
for more complex sounds.

INTENSITY AND PRESSURE

The overall amplitude of a sound wave is typically
quantified and measured in units of sound pres-
sure or sound intensity to describe how the sound

FIGURE 3–12. Illustration of pure tones of the same
frequency with different amplitudes. notice how the
period of the vibration is the same for all three wave-
forms and only the height of the waveforms is different.

FIGURE 3–13. Quantication of amplitude by the
method of root mean square (RMS). The instantaneous
amplitudes across the waveform are squared to re-
move the negative numbers, then averaged to nd the
mean, and nally the square root of the number is de
termined to get the total RMS value.

FIGURE 3–14. Illustration of how amplitude can be de-
scribed based on its peak (Ap) and peak-to-peak (Ap-p)
values. The RMS amplitude is equal to 0.707 × Ap.

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3. PRoPERTIES oF SoUnD 29

SYNOPSIS 3–1

l The back and forth vibration of a sound source sets up alternating areas where
the air molecules are pushed together, called condensation, and areas where the
air molecules are pulled apart, called rarefaction. The air molecules move
only within a small localized area, but the condensation and rarefaction areas
are passed to adjacent air molecules, which cause the waveform’s pressure
variations to move through the medium. Sound waves travel in air at a speed of
about 343 m/s (at 680 F).

l Simple vibrations, called pure tones, sine waves, or sinusoids, are characterized
by their physical (acoustic) dimensions of frequency (or period), amplitude, and
starting phase.

l The frequency of a sound refers to the number of vibrations that occur in
1 second and has units of hertz (Hz) or kilohertz (kHz); 1 kHz = 1000 Hz.
The reciprocal of frequency is the period (T), which is the time it takes to
complete one cycle of vibration and has units of seconds (s) or milliseconds
(ms) (1 ms = 1/1000 s). If either the frequency or period is known, the other
can be calculated (f = 1/T or T = 1/f ).

l The frequency range for human hearing is about 20 to 20,000 Hz. other
species may be sensitive to other frequency ranges.

l The starting phase of a sound refers to what position in the cycle a vibration
begins its cycle, and is expressed in units of degrees around a circle (0 to 360º).
For example, a vibration that begins at its equilibrium and moves toward its
area of maximum condensation has a starting phase of 0º; a vibration that
begins at the point of maximum rarefaction and moves toward equilibrium has
a starting phase of 270º.

l For a single pure tone, humans cannot tell the difference between starting
phases. Combining two or more pure tones of the same frequency, but with
different starting phases, results in different phase relations at different points
in time (instantaneous phase) and produces a complex waveform that is the
sum of the two waveforms. Two pure tones of the same frequency that are
180º out of phase will cancel each other out and not produce any sound.

l The amplitude of a sound refers to how far an object moves back and forth
and/or the amount of maximum and minimum air pressure created. The
larger the movement or pressure variation, the greater the amplitude for any
given frequency. A simple way to describe amplitude of a visually displayed
waveform is to measure the distance or pressure between the highest point
of condensation peak and the lowest point of rarefaction peak, called peak-to-
peak amplitude (Ap-p). Measures can also be made between the condensation or
rarefaction peak to the equilibrium point, called peak amplitude (Ap). A more
practical measure is called root-mean-square (RMS) amplitude, which is the
way that instruments measure a sound’s overall amplitude. The RMS method
averages the amplitudes across the entire waveform by squaring each value (to
remove all negative values), then averaging these squared values, and nally
taking the square root to bring it back into scale.

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AUDIOLOGY: SCIENCE TO PRACTICE

energy is distributed over some area of the prop-
agating wave. For any given sound wave, there is
a corresponding sound intensity and sound pres-
sure. If you know either the intensity or the pres-
sure, the other quantity can be derived. Intensity
and pressure are related to each other by the fol-
lowing formulas:

I = p 2

p = √I

It should be intuitive that the farther away you
are from a sound’s source, the softer it will be-
come. As the sound gets further away from the
sound source (assuming there are no obstruc-
tions), it is distributed over a greater spherical
area, as illustrated in Figure 3–15.

The decrease in a sound’s intensity with dis-
tance is known as the inverse square law. The
inverse square law states that the intensity (I) is
inversely (decreases) related to the square of the
distance between any two points (D), and is ex-
pressed by the following formula:

I = 1/D 2, where D = d1 /d 2

For example, if the distance is doubled (D = 2; d1/
d2 = 2/1), the intensity decreases by one-fourth
(I = 1/22). Now let’s see how that same sound’s
pressure ( p) would change with distance. Be-
cause of the previously discussed relation be-

tween intensity and pressure for any given
sound wave, the inverse square law for pressure
is obtained by substituting p 2 for I in the above
formula, which results in the following formula
to describe how pressure changes with distance:

p2 = 1/D 2

p = 1/D, where D = d1 /d2

This formula says that the sound pressure is in-
versely (decreases) related to the distance be-
tween two points (D), rather than the square of
the distance that was used for intensity. For exam-
ple, if the distance is doubled (D = 2; d1/d2 = 2/1),
the pressure decreases by one half ( p = 1/2).

Sound intensity is actually a measure of
power that is distributed over an area, and has
units of watts/m2 or watts/cm2 depending on
the system of measurement being used (MKS or
CGS). Sound pressure is a measure of force dis-
tributed over an area and has units of dynes/cm2,
newton/m2, or micropascals (µPa) depending on
the system of measurement being used. For this
text, we will only use units of watts/m2 for inten-
sity and µPa for pressure. For our purposes, we
are most interested in the range of sound intensi-
ties or pressures that are audible, that is, from the
smallest amount needed to barely hear a sound,
up to the largest amount that the ear can toler-
ate. Based on accepted standards derived from
the lowest average levels (thresholds) obtained
from young adults, the lowest average intensity
needed to hear a sound, called the reference level
for intensity, is 0.000000000001 w/m2 (or 1.0 ×
10−12 w/m2). The lowest average pressure needed
to hear a sound, called the reference level for
pressure, is 20 µPa (or 2.0 × 101 µPa). Remark-
ably, these lower levels of audition correspond
roughly to a vibration about the size of a hydro-
gen molecule (Gelfand, 2009). The highest inten-
sity (also called the threshold of pain) that can
be tolerated is approximately 100 w/m2 (or 1.0 ×
102 w/m2). The highest pressure that can be toler-
ated is approximately 200,000,000 µPa (or 2.0 ×
108 µPa). As you can see, the upper tolerated limit
of sound intensity is 100,000,000,000,000 (or
1014) times greater than the least audible sound
(i.e., from 1.0 × 102 w/m2 to 1.0 × 10−12 w/m2). For

2 D

3 D

FIGURE 3–15. Illustration of how the energy of a
sound is distributed over a larger area as the distance
from the sound source is doubled and tripled, and is
the basis for the inverse square law.

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3. PRoPERTIES oF SoUnD 31

pressure, the upper tolerated limit is 10,000,000
(or 107) times greater than for the least audible
sound (i.e., from 2.0 × 101 µPa to 2.0 × 108 µPa).
Recall that intensity and pressure are related
by p = √I; therefore, it follows that the range of
pressures (107) is equal to the square root of the
range of intensities (√1014 = 107).

Table 3–2 summarizes the intensity and pres-
sure ranges for the human ear. It may have struck
you by now that these amplitude ranges are quite
large, and it would be quite cumbersome if you
were trying to graph them on a linear scale ( y-axis).
Fortunately, linear scales can be transformed into
ratio scales, as described in the next section on
decibels, and makes working with intensity and
pressure ranges much more manageable.

DECIBELS

To avoid linear scales of intensity or pressure
ranges that would require working with large
numbers or scientific notation, we transform these
scales into a more manageable scale called the
decibel scale. Any decibel scale is a ratio scale in
which a measured value is related to a specified
reference value. For example, as was mentioned
above, the most intense sound that can be toler-
ated is 1014 times greater than the lowest sound
intensity that can be heard. If we consider the
lowest audible sound intensity as the reference,
this least audible sound could be expressed as
1 or 100; then the range of sound intensity can
be written as a ratio of 1014/100. The next step

in the transformation to a decibel scale is to take
the logarithm3 (or log) of that ratio, the Bel. The
log is the mathematical difference in the values
of the exponents in the ratio. Stated another way,
the log is the power to which 10 must be raised to
produce the number defined by the ratio. In our
example, the mathematical difference in the expo-
nents is 14 (14-0), which means that the range for
intensity, in Bels, would be from 0 (least intense)
to 14 (most intense). The upper limit would be
the same as saying that 10 must be raised to the
14th power (1014). Because the range for Bels
only goes from 0 to 14, it is considered too re-
strictive to effectively describe the range of audi-
ble sounds; thus, to expand the range, the Bel is
multiplied by a factor of 10 and is called the deci-
bel (dB). The decibel equation can be written as:

dB = 10 log (Xmeas /Xref )

where Xmeas equals the sound that is being mea-
sured, and Xref equals the reference sound to
which Xmeas is to be compared. It is important to
see that when the measured value is the same as

3 A logarithm of a number, in base 10 (log10), is the
power to which 10 must be raised to obtain that num-
ber. Some simple examples are for powers of 10, in
which the exponent is the log; for example, the log of
1000 or 103 = 3. It is also important to remember that
the log (1) = 0. Another useful example that you may
want to memorize is log (2) = 0.3. Calculators can be
used to find logs of other less obvious numbers. Other
sources, such as Speaks (2017), should be consulted
for a review of logarithms.

TABLE 3–2. Intensity and Pressure Ranges from the Least Audible (Reference Level) to the
Upper Limit that Is Tolerated (Pain Threshold)

Intensity (w/m2)a Pressure (μPa)b

Upper limit (pain) 100 or 1 × 102 200,000,000 or 20 ×107

(or 2.0 × 108)

Lowest audible
(reference level)

0.0000000000001 or 1 × 10–12 20 or 20 ×

100

(or 2.0 × 101)

aWatts per square meter.
bMicroPascals.

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AUDIOLOGY: SCIENCE TO PRACTICE32

the reference value, that is, Xmeas /Xref = 1, the mea-
sured value would be equal to 0 dB because the
log of 1 (or log 100) is equal to zero. Applying a
decibel conversion to describe the range of sound
intensity, the upper limit of intensity would be
140 dB greater than the least audible intensity, as
determined by the following calculation:

dB intensity (at upper limit)

= 10 log (1014/100)
= 10 log (1014)
= 10 (14), where log of 1014 equals 14
= 140 dB

The formula for converting to decibels can be ap-
plied to anything that can be expressed as a ratio
if the reference value is known. For example, we
could calculate the decibel difference between a
large bag of oranges (Xmeas) as compared with a
small bag of oranges (Xref). If there are twice as
many oranges in the larger bag than the smaller
bag, there would be 3 dB more oranges in the
larger bag than in the smaller bag, as shown in
the following calculation:

dB in bag of oranges with twice as many as
the reference bag:

= 10 log (2/1)
= 10 log (2)
= 10 (0.3), where log of 2 equals .3
= 3 dB

Decibels of Intensity Level (dB IL)

Let’s look at another example and calculate how
many dB some arbitrary measured intensity is
above the lowest average intensity needed to
hear. In other words, how much more intense
is this measured higher intensity level above the
lowest possible audible intensity? Recall that the
lowest average intensity needed to hear a sound,
called the standard reference level for intensity,
is 1 × 10−12 w/m2 (or simply 10–12 w/m2). Let’s say
we measure a sound intensity to be 1 × 10−6 w/m2.
The calculation of dB intensity is:

dB intensity = 10 log (10−6 w/m2/10−12 w/m2)

Whenever the standard reference value for in-
tensity (10−12 w/m2) is used or implied in the de-
nominator of the decibel formula, this is called
decibel intensity level (dB IL). The general equa-
tion for dB IL is:

dB IL = 10 log (Imeas w/m2/10−12 w/m2).

When the measured intensity is the same as the
reference level for intensity (10−12 w/m2/10−12
w/m2), in decibels this would be the 10 log (1),
which would become 0 dB IL. By using a deci-
bel scale, we can define the intensity range of
human hearing from 0 to 140 dB IL. It is impor-
tant to realize that 0 dB IL does not mean the ab-
sence of sound; it only means that the measured
sound intensity is the same as the standard refer-
ence intensity. However, as you will see later, the
lowest audible intensity is different depending
on frequency, type of earphones, and other spec-
ified listening conditions, but all these variations
are always referenced to the universally accepted
standard reference intensity of 1.0 × 10–12 w/m2.

Now let’s look at some other examples. Sup-
pose you make a sound measurement and find
it to be 10−5 w/m2 (0.00001 w/m2). How many
dB IL is this sound? The calculation is as follows:

dB intensity level (dB IL) for a measured
sound = 10−5 w/m2

= 10 log (10−5 w/m2/10−12 w/m2)
= 10 log (107)
= 10 (7), where log of 107 equals 7
= 70 dB

The decibel can be used to describe the ratio of
any two numbers if the proper reference value
is specified in the denominator. Suppose you are
interested in expressing, in dB, how the inten-
sity of one sound compares with the intensity
of another sound. For example, assume that one
sound has an intensity that is 10,000 times more
intense than another sound. In this case, the less
intense sound can be considered the reference
and written as 1 in the denominator; the ratio of
these two sounds would be 10,000/1 (i.e., with-
out needing to use the 10−12 w/m2). The dB of the
louder sound, as referenced to the softer sound,
is calculated as follows:

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3. PRoPERTIES oF SoUnD 33

dB intensity of a sound 10,000 times greater
than another sound

= 10 log (10,000/1)
= 10 log (104)
= 10 (4), where log of 104 equals 4
= 40 dB

As another example, if the intensity of a sound is
doubled, how many dB has that sound increased?
In this example, the increase in intensity can be
thought of as a ratio of 2/1 (the louder sound is
twice as intense as the softer sound) and, there-
fore, would show an increase of 3 dB. The calcu-
lation is as follows:

dB intensity of a sound twice as much as
another sound (increase)

= 10 log (2/1)
= 10 (0.3), where the log of 2 equals 0.3
= 3 dB

This concept and use of the formula would also
apply if one were to decrease the intensity level
of a sound. For example, if one sound is half the
intensity of another sound, the ratio would be
1/2. The calculation is as follows:

dB intensity of a sound half as much
as another sound (decrease)

= 10 log (1/2)
= 10 (–0.3), where the log of 2 equals –0.3
= –3 dB

If you find it easier, the above example could be
calculated using a ratio of 2/1, but then be sure
to indicate that it is negative (representing a de-
crease): Notice that in both cases, the answer is
3 dB (either positive or negative).

Decibels of Sound Pressure
Level (dB SPL)

In audiology, decibels of sound pressure are
commonly used. To derive the decibel scale for
sound pressure, it is important to go back to the
previous relation between pressure and inten-

sity (I = p 2). This relation requires that pressure
squared ( p 2) be substituted for intensity (I ) in the
general equation for decibels. The derivation is
as follows:

dB sound pressu

= 10 log (p2meas /p2ref)
= 10 log (pmeas /pref)2

= 20 log (pmeas /pref), where log (x)2 equals
2 log (x)

Notice that for dB of sound pressure, the log of
the pressure ratio is multiplied by 20 instead of
by 10 that was used for dB of sound intensity.
Using the formula for dB of sound pressure,
any pressure ratio can be expressed in decibels.
The decibel scale for sound pressure would also
range from 0 to 140 dB because the upper limit
for pressure is 107 times greater than the lowest
pressure. The calculation is expressed as follows:

dB pressure (at upper limit)

= 20 log (107/100)
= 20 log (107)
= 20 (7), where log of 107 equals 7
= 140 dB

Recall that the standard reference sound pres-
sure level is 20 µPa. When a measured pressure
is compared to this standard reference pressure,
that is, when the specific reference value for
sound pressure is used or implied in the denom-
inator of the formula for dB sound pressure, this
is called decibel sound pressure level (dB SPL).
The formula for dB SPL is:

dB SPL = 20 log (Pmeas µPa/20 µPa)

Whenever the measured sound pressure is equal
to the standard reference level for sound pressure
it would be equal to 0 dB SPL (i.e., 20 log [1] = 0).
Using dB SPL, we have now defined the range of
human hearing from 0 to 140 dB SPL. It is impor-
tant to realize that 0 dB of sound pressure does
not mean the absence of sound pressure; it only
means that the measured sound pressure is the
same as the standard reference sound pressure. A
sound that is 0 dB SPL has the same pressure as

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AUDIOLOGY: SCIENCE TO PRACTICE34

the standard reference pressure of 20 µPa. How-
ever, as with intensity, the lowest audible pres-
sure can depend on frequency, type of earphones,
and other specified listening conditions, but these
are always referenced to the universally accepted
standard reference pressure of 20 µPa.

Let’s look at some other decibel examples us-
ing pressure. Suppose you make a sound measure-
ment and find it to be 200,000 µPa. What is the
dB SPL of this sound? The calculation is as follows:

dB sound pressure level (dB SPL) for a
measured sound = 200,000 µPa

= 20 log (200,000 µPa/20 µPa)
= 20 log (104)
= 20 (4), where log of 104 equals 4
= 80 dB SPL

What if you want to compare one sound to an-
other sound? For example, suppose the pressure
of one sound is 1000 times more than the pres-
sure of another sound. This defines the pressure
ratio of these two sounds, that is, 1000/1. In dB
pressure, this is expressed using the following
equation:

dB pressure of a sound 1000 times greater
than another sound

= 20 log (1000/1)
= 20 log (103)
= 20 (3), where log of 103 equals 3
= 60 dB

How about the situation in which we double the
pressure of a sound? How many dB greater is the
louder sound? The calculation is as follows:

dB pressure for a sound twice with as much
(doubling) as another sound (increase)

= 20 log (2/1)
= 20 (0.3), where the log of 2 equals 0.3
= 6 dB

As was discussed above for intensity, this would
similarly apply if one were to decrease the pres-
sure level of a sound. For example, if one sound
is half the pressure of another sound, the ratio

would be 1/2 (softer sound is half the pressure
level of the louder sound). The calculation is as
follows:

dB pressure of a sound half as much as
another sound (decrease)

= 20 log (1/2)
= 20 (–0.3), where the log of 2 equals –0.3
= –6 dB

Notice that if the pressure of a sound is
doubled, it increases by 6 dB, whereas if the
intensity of a sound is doubled, it increases by
3 dB. However, it is important to realize that for
a specific sound, the intensity and pressure must
vary together (I = p 2), that is, one cannot dou-
ble the sound’s pressure and at the same time
double that sound’s intensity. For example, if we
double the intensity of a sound, the decibel level
increases by 3 dB and the pressure also increases
by 3 dB because the sound’s pressure would in-
crease by the square root of two. On the other
hand, if we double the pressure of a sound, the
decibel level increases by 6 dB and the intensity
of that sound also increases by 6 dB because the
sound’s intensity is squared. These comparisons
can be illustrated by the following calculations
(keeping in mind that I = p 2); (a) the pressure
of a sound is doubled, and (b) the pressure of a
sound is increased by a factor of 10:

(a) dB pressure increase dB intensity increase

= 20 log (2/1) = 10 log (22/1)
= 20 log (2) = 10 log (4)
= 20 (0.3) = 10 (0.6)
= 6 dB = 6 dB

(b) dB pressure increase dB intensity increase

= 20 log (10/1) = 10 log (102/1)
= 20 log (10) = 10 log (100)
= 20 (1) = 10 (2)
= 20 dB = 20 dB

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3. PRoPERTIES oF SoUnD 35

Table 3–3 summarizes how the ranges of pres-
sure and intensity for human hearing are related
and how the linear scales are transformed into
their respective decibel (ratio) scales. The deci-
bel is defined as 10 times the log of an intensity
ratio and 20 times the log of a pressure ratio. The
decibel range between the least audible sound
and the upper limit (threshold of pain) is 140 dB
for either intensity or pressure. However, a ten-
fold increase in intensity results in a 10 dB in-
crease, whereas a tenfold increase in pressure
results in a 20 dB increase because of the rela-
tion between intensity and pressure ( p = √I ). For
more information on and practice with decibels,
see Audiology Workbook (Kramer & Small, 2019)
or the textbook by Speaks (2017).

Combining Levels from Different
Sound Sources

One thing to keep in mind is that decibels cannot
be simply added or subtracted, that is, adding a
sound of 40 dB to another sound of 40 dB does
not equal 80 dB; the decibels must be converted
back to intensity before being combined. Let’s
look at what happens to the level of a sound
when you combine two or more sound sources,
each producing the same or different levels. The
most important thing to keep in mind is that
when combining sounds, you should work with
the intensity levels of the sounds that combine
(not the pressures); therefore, the standard deci-
bel formula for intensity, 10 log (Imeas /10–12 w/m2)
must be used. However, as you learned earlier “a
dB is a dB,” and the combined level you obtain for
dB IL would be the same in dB SPL. Since we
more often measure sounds in dB SPL, the fol-
lowing examples will have the levels in dB SPL;
however, it is the actual intensity levels (not in
dB) that must be added together. In the case
where all the sound sources have equal output
levels, you can treat this like examples discussed
earlier in which the combined level can be calcu-
lated by taking the log of the number of sources
(added to the level of one source). In other
words, if there are three sources with equal lev-
els, the combined output (in dB) is calculated as
follows:

Combined (dB SPL or IL) = x dB from
1 source + 10 log (3/1)

Example: You have three fans, each with an out-
put level of 72 dB SPL. What is the combined
level of the three fans? The solution is as follows:

dB combined = 72 + 10 log (3/1)

= 72 + 10 (0.48), where log of 3 = 0.48
= 72 + 4.8
= 76.8 dB SPL (or dB IL)

It is a bit more difficult when combining sound
sources with different output levels. To do this,
you must: (1) calculate the intensity level (not in
dB) of each source; (2) add them together to get
the combined numerator of the intensity ratio
(Imeas), and; (3) calculate the dB level using the
formula for intensity level. The tricky part is cal-
culating the intensity levels of the sounds, akin
to finding the antilog, i.e., that is, what is the
numerator of the intensity ratio for a given dB
level. The general formula for calculating the Imeas
for each source when the dB level is specified is
as follows:

x dB (given) = 10 log (Imeas w/m2/10–12 w/m2);
then solve for Imeas.

Example: You have two radios, one with an out-
put of 80 dB SPL and the other with an output
of 70 dB SPL. What is the combined level of the
two radios? The solution is as follows:

1) Radio 1: 80 dB SPL = 10 log (Imeas/10–12) or
8.0 = log (Imeas/10-12)

Imeas = 1 × 10–4; determined so that the addi-
tion of exponents would = 108

2) Radio 2: 70 dB SPL = 10 log (Imeas/10–12) or
7.0 = log (Imeas/10–12)

Imeas = 1 × 10–5 ; determined so that the addi-
tion of exponents would = 107

3) Convert Radio 2 so it has the same
exponent as Radio 1 (10–4):

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T
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3. PRoPERTIES oF SoUnD 37

Radio 2: 1 x 10–5 = .1 x 10–4 (multiply expo-
nent x 10; therefore, divide 1 by 10)

4) Combine the intensities from each radio:

(1 × 10–4) + (.1 × 10–4) = 1.1 × 10–4

5) Calculate the dB level from these
combined levels:

= 10 log (1.1 × 10–4/10–12)
= 10 log (1.1 × 108)
= 10 log (1.1) + log (108)
= 10 (0.04 + 8)
= 80.4 dB SPL (or IL)

AUDIBILITY BY FREQUENCY

As mentioned earlier, the human ear is respon-
sive to frequencies from 20 to 20,000 Hz; how-
ever, the ear is not equally sensitive across the
frequency range. The relation between normal
thresholds (in dB SPL) and frequency is referred
to as the threshold of audibility curve. Fig-
ure 3–16 shows an example of a threshold of
audibility curve from 100 to 10,000 Hz. As you
can see, humans are most sensitive to frequen-
cies between 500 and 2000 Hz, and it takes
slightly higher dB SPLs to reach threshold in the
lower and higher frequencies. Also shown in Fig-
ure 3–16 is an estimate of the upper limit for
hearing, called the threshold of pain. Notice that
the upper limit does not vary much as a function
of frequency, probably because it involves the
threshold of feeling within the tympanic mem-
brane, which is relatively constant across fre-
quency (Durrant & Lovrinic, 1995; Kent & Read,
2002). The area between the lower threshold
curve and the upper pain limit curve defi nes the
useable range for human hearing. However, most
listeners fi nd sounds above 100 dB SPL uncom-
fortably loud. Many loud music venues may have
sound levels on the order of 110 to 120 dB (and
may damage hearing!).

WAVELENGTH

An additional acoustic parameter is the distance
that pure tones travel in one cycle, the wave-
length. The symbol for wavelength is the Greek
symbol λ (lambda). The wavelength has a unit
of length (e.g., feet, meters) rather than unit of
time, which is used to defi ne a pure tone’s period.
Wavelength is a measure of the distance between
one point on the waveform to the same point
on the next cycle, most easily seen as the dis-
tance between adjacent points of condensation
(or rarefaction) in Figure 3–1. You should be able
to surmise that higher frequencies have shorter
wavelengths than lower frequencies because the
cycles are closer together. Since the speed of
sound is determined by the properties of the air,
and is the same for all frequencies, wavelength
can be defi ned by the following equation:

Threshold of Pain

100 1,000 10,000
Frequency (Hz)

S
ou

nd
P

re
ss

ur
e

(d
B

S
P

Threshold
of Hearing

Sound not
audible to
human ear

140

120

100

-20

FIGURE 3–16. Thresholds and upper range of hearing
as a function of frequency in humans. The variation in
thresholds (in dB SPL) as a function of frequency is
called the threshold of audibility curve. In this example,
the closed circles represent the threshold reference
levels based on American national Standards Institute
[ANSI] (2010). Higher dB SPLs are needed in the low
and high frequencies to reach threshold than in the
middle frequencies. The threshold of pain (140 dB SPL)
is also shown; although most listeners do not tolerate
levels above 100 dB SPL.

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AUDIOLOGY: SCIENCE TO PRACTICE38

SYNOPSIS 3–2

l Intensity (w/m2) and pressure (µPa) are related to each other by the equation
p = √I (or I = p2). In audiology, pressure is usually used to quantify the level
(amplitude) of sounds. The minimum mean sound pressure for audibility, called
the reference level for pressure, is 20 µPa. The mean upper limit of pressure
that can be tolerated is 20 × 107 µPa. For intensity, the reference level is 1012
w/m2 and the mean upper limit is 102 w/m2. The range of hearing from the
lowest to the highest is 107 for pressure and 1014 for intensity (notice the relation
107 = √1014). In either case, the range on a linear scale is too cumbersome to be
very useful, so the ranges are converted to decibel (dB) scales.

l Decibel scales are based on a logarithmic (log) scale. The log of a number (x) is
dened as the power to which 10 must be raised to be equal to the number (x).
Stated another way, the exponent of a number is the log of that number. Most
calculators can easily calculate the log of any number. Some simple examples to
keep in mind are:

log (1014) = 14
log (107) = 7
log (102) = 2
log (1) = 0
log (2) = 0.3
log (4) = log (2) + log (2) = 0.6

l A decibel (dB) is dened as 10 times the log of the ratio of two numbers [10 log
(Xmeas/Xref)]. This formula is directly applicable to the ratio scale for intensity level
[10 log (Imeas/Iref)]; however, because I = p 2, the conversion to decibels for sound
pressure follows basic rules of logs and becomes dened as 20 times the log of
the ratio of two pressures [20 log (Pmeas/Pref)]. When the reference (denominator)
for the ratio is 20 μPa it is called dB sound pressure level (dB SPL). When the
reference for the ratio is 10–12 w/m2, it is called dB intensity level (dB IL).

l When the measured sound pressure or sound intensity is equal to its respective
reference level (giving a ratio of 1/1), it would be equal to 0 dB because the log of
1 = 0. The range of hearing in decibels is 140 dB for either pressure or intensity
as calculated for dB pressure = 20 log (107) or dB intensity = 10 log (1014).

l Sound pressure increases by 6 dB when the pressure is doubled [20 log (2/1)].
Sound intensity increases by 3 dB when the intensity is doubled [10 log 2/1].
A sound that is 100 times greater in pressure than another sound would be
40 dB greater; a sound that is 100 times greater in intensity than another sound
would be 20 dB greater. However, since you cannot simultaneously double the
intensity and double the pressure of the same sound (recall that I = p2), the
number of decibel change would be the same for pressure and intensity.

l The inverse square law denes how the intensity or pressure of a sound
changes with distance. As the distance increases, the sound energy spreads out
in a spherical form, and the decrease in the level of the sound can be described
for intensity as I = 1/D 2 or for pressure as p = 1/D, where D is the ratio of the
distance between two sounds (d1/d2). For example, if one doubles the distance,
the intensity would decrease by 1/4 (or –6 dB) and the pressure would decrease
by 1/2 (or –6 dB).

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3. PRoPERTIES oF SoUnD 39

λ = c/f, where c is the speed of sound
and f is the frequency.

This equation shows that as frequency gets
higher, the wavelength gets shorter. For example,
a 2000 Hz pure tone, traveling in air (c = 343 m/s),
has a wavelength of 0.17 m (or about 0.56 feet),
whereas a 250 Hz sinusoid traveling in the same
air would have a wavelength of 1.32 m (or about
4.5 feet). The same pure tones traveling in water
would have wavelengths that are approximately
four times longer because the speed of sound in
water is about four times faster than in air. Con-
versely, if you know the wavelength of a sound,
the frequency can be calculated by the equation:

f = c/λ.

The wavelength, to some extent, determines how
a sound is affected as it encounters objects in
its path. In a simple sense, the longer a sound’s
wavelength is relative to the size of the object en-
countered, the less likely the object will have an
effect on the sound. However, if the wavelength
is short (as for higher frequencies) relative to the
size of an object, then the object will tend to
block (and reflect) the sound. You may have no-
ticed that it is much easier to hear drums over a
greater distance than the higher frequency band
instruments, like a flute; this is partly due to the
higher frequencies being blocked by objects
along the way, whereas the lower frequencies
more easily go around the objects. As we will
also see later in this chapter, part of our abil-
ity to localize sounds is related to the different
amplitudes that occur between the two ears for
higher frequencies, which tend to be blocked by
the head because of their shorter wavelengths.

COMPLEX SOUNDS

As mentioned earlier, most sounds we listen to
are complex sounds, which means that they are
the result of combining two or more individual
pure tones. Any complex vibration can be cre-
ated or described by knowing the frequencies
(or periods), amplitudes, and starting phases of
the individual pure-tone components. The num-
ber of pure tones, along with their relative ampli-
tudes and starting phases, will determine the type
of sound we hear. A spectrum (plural = spectra) is
a way to describe a complex vibration by plotting
a graph that shows the amplitudes as a function
of frequency, called a frequency spectrum, or the
starting phases as a function of frequency, called
a phase spectrum. Figure 3–17 shows an example
of a complex vibration that is composed of two
different pure tones with amplitudes and phases
shown in the corresponding spectra. The ampli-
tude spectra of complex periodic vibrations, as
shown on the right side of Figure 3–17, show ver-
tical lines at the discrete frequencies that make
up the vibration, and this type of spectrum is
called a line spectrum.

Vibrations are generally classified as peri-
odic or aperiodic. A periodic vibration is one in
which the vibratory pattern repeats at regular in-
tervals. A pure tone (sinusoid) is an example of a
simple periodic vibration. However, when two or
more pure tones are combined into a nonsinusoi-
dal pattern they may also be considered periodic
if the wave pattern repeats itself as a function of
time. These nonsinusoidal periodic vibrations are
called complex periodic vibrations (or complex
periodic tones). Complex periodic vibrations typ-
ically have a tonal or buzzing quality. The low-
est frequency component in a complex periodic

SYNOPSIS 3–2 (continued )

l When combining output levels from more than one source (whether specied
in dB IL or dB SPL), it is the intensity levels (w/m2) that are combined; therefore,
the formula 10 log (Imeas/10–12 w/m2) must be used. If sounds are unequal,
rst calculate Imeas for each sound, then combine the Imeas from each sound
(converting exponents to be the same), then calculate the dB of the combined
Imeas relative to 10–12 w/m2.

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AUDIOLOGY: SCIENCE TO PRACTICE

vibration is called the fundamental frequency (f0).
Integer multiples of the fundamental frequency
are called harmonics, such as 1f0, 2f0, 3f0, and
so forth. Generally, complex periodic vibrations
occur when harmonically related pure tones
are combined. For example, combining 100 Hz,
200 Hz, 300 Hz, and 400 Hz will produce the com-
plex periodic waveform shown in Figure 3–18. If
additional sequential harmonics were added to
those shown in Figure 3–18, the resulting wave-
form would smooth out the smaller bumps and,
with enough harmonics, would produce what is
called a sawtooth waveform. A sawtooth wave-
form is a complex periodic waveform that has
more of a buzzing sound quality rather than a
tonal quality. You can see in Figure 3–18 that the
longest period of this complex periodic wave-
form is the same as the lowest frequency compo-
nent (100 Hz). The fundamental frequency usu-
ally determines the primary pitch of the sound,
but the other components can also be heard and
will contribute to the perception/quality of the
complex periodic vibration. Adding different
combinations of pure tones and using different
amplitudes or phases can affect the overall shape
of complex periodic waveforms.

On the other hand, aperiodic vibrations are
those in which the pattern of vibration does not
regularly repeat itself over time; in other words,
there is no periodicity in the wave pattern. The
waveform shown in Figure 3–19 is an example
of an aperiodic vibration. Aperiodic vibrations
are generally called noise. Noise is produced by
combining many pure tones with random start-
ing phases. When there are an infi nite number
of frequencies with random phases and equal
amplitudes over the entire frequency range it is
called white noise (analogous to white light). The
spectrum shown on the right side of Figure 3–19
is a horizontal line, rather than discrete vertical
bars, to indicate that there are infi nite frequencies
present over the indicated range, and this type of
spectrum is called a continuous spectrum.

Aperiodic noise-type vibrations are encoun-
tered frequently in our environment, including
many speech sounds (e.g., /s/, /sh/, /f/, /th/), as
well as sounds produced by things such as run-
ning water, rustling leaves, or engines. In addi-
tion, many sounds we listen to have components
that give it a tonal (periodic) quality as well as
a noise (aperiodic) quality, such as the speech
sounds (/v/, /z/, /j/) or the different pitches as-
sociated with the buzzing of different types of

FIGURE 3–17. Example of a complex periodic wave-
form composed of two frequencies (left), which are
described by their corresponding amplitude spectrum
(top right) and starting phase spectrum (bottom right).
These types of spectra are called line spectra.

Time (ms)
0 5 10 15 20

A
m
pl
itu
de
(
ar
bi
tr
ar
y)

-8
-6
-4
-2
0
2
4
6
8

A
m
pl
itu
de
(
ar
bi
tr
ar
y)

0
1
2
3
4
5
6
7
8

Frequency (Hz)

P
ha

se
0

100 100 200 00 300 00 400

Frequency Hz

100 100 200 00 300 00 400
Frequency Hz

FIGURE 3–18. Example of a complex periodic wave-
form with a fundamental frequency of 100 Hz and its
harmonics, 200 Hz, 300 Hz, and 400 Hz. With addi-
tional sequential harmonics added, the resulting wave-
form would be a sawtooth waveform.

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3. PRoPERTIES oF SoUnD 41

motors. In some of these latter cases, the under-
lying periodicity or the frequency range of ape-
riodic combinations will determine the overall
perceptions. If we know the frequencies (or pe-
riods), amplitudes, and starting phases of all the
individual components of a complex periodic or
aperiodic vibration, we can construct the pre-
dictable vibration pattern that would result from
their combination. Instruments are available that
can perform a fast Fourier transform (FFT) on
complex vibrations to determine the frequencies,
amplitudes, and starting phases of the individual
components. Figure 3–20 shows some additional
examples of complex vibrations with their corre-
sponding amplitude spectra.

RESONANCE

The frequencies to which objects vibrate most
easily are called resonant (or resonance) fre-
quencies. You are undoubtedly familiar with this
concept when you think about musical instru-
ments, such that strings of different length vi-
brate best at certain frequencies, or the smaller
violin’s sounding board emphasizes higher fre-
quencies compared with the much larger bass,
which emphasizes the lower frequencies. In the
case of a guitar string that is attached at both
ends, when plucked, there are waves that move
toward the ends of the strings and are then re-
flected back. This interaction of the two waves
(incident and reflected) results in places where
the displacements cancel each other, called nodes,
and places where they combine with each other,
called antinodes. For the guitar string, there are
nodes at both ends (where the string cannot
move) and an antinode at the center of the string
that produces the string’s primary musical note.
The pattern of vibration between the nodes at
the ends of the string and the antinode in the
middle of the string is half of a cycle, as shown in
Figure 3–21A. These patterns of displacement as
a function of distance along the string are related
to the frequency’s wavelength (λ). The longest
wavelength determines the string’s primary reso-
nant frequency (a.k.a. first mode or fundamental
frequency) and is equal to half of a wavelength
(λ/2). For a given length of string, the fundamen-
tal frequency can be calculated as:

f0 = c/2L, where c = speed of sound;
L = length of string.

The string analogy and other vibrating objects
have additional modes (e.g., harmonics) of vibra-
tions that create other possible nodes and an-
tinodes, corresponding to f2, f3, f4, and so on, as
illustrated in Figure 3–21B and C. When a reso-
nating source has a fundamental frequency that
is equal to one-half of a wavelength, it is called
a half-wave resonator, and generates a specific
fundamental frequency based on its character-
istics, and also generates harmonics at integer
multiples of the fundamental frequency.

FIGURE 3–19. Example of an aperiodic noise vibration
(left) and its corresponding amplitude spectra (right).
These types of spectra are called continuous spectra.

Pure tone

Square Wave

White Noise

Click

Tone Burst

Waveform Spectrum

Time (ms)

Frequency (kHz)

1 2 3 4 5 6 7 8 9 100 1 2 3 4

+5
0

-5

5
0

+5
0
-5
10
5
0
+5
0
-5
10
5
0
+5
0
-5
10
5
0
+5
0
-5
10
5
0

FIGURE 3–20. Examples of some continuous and
transient signals with their corresponding amplitude
spectra.

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AUDIOLOGY: SCIENCE TO PRACTICE42

Resonance also occurs in tubes of different
dimensions whereby the air molecules within
the tube interact and produce regions of nodes
and antinodes within the tube depending on the
length of the tube. For example, blowing across a
small tube produces a higher pitched tone com-
pared with a lower pitched tone from a longer
tube. The relationship of nodes and antinodes
will depend also on whether the tube is open
on both ends or only on one end, as illustrated
in Figure 3–22. For the same-length tube, being
open on both ends produces a higher-pitch tone
than one open on only one end because of the
different relationships of nodes to antinodes as
illustrated in Figure 3–22A. As with the string ex-
ample, a tube open at both ends involves half of a
wavelength, and the resonant frequency can also
be obtained by the formula f0 = c/2L. This would
also be a half-wave resonator with a fundamen-
tal frequency and harmonics at integer multiples
of the fundamental frequency. Let’s now look at

a tube that is open only on one end (thinking
ahead to our vocal tract or ear canal that acts
much like a tube open at one end). As shown in
Figure 3–22B, there must be a node at the closed
end and an antinode at the open end. For a tube
that is open only on one end, a one-quarter wave-
length can fit within the tube (between nodes
and antinodes). This type of resonator is called a
quarter-wave resonator, and generates a specific
fundamental (f0), but the harmonics are only at
odd multiples of the fundamental frequency. The
resonant frequency of a quarter-wave resonator
is calculated as:

f0 = c/4L, where c = speed of sound;
L = length of tube.

Node

Antinode

Antinode
Node

Antinode

Antinode Antinode

Antinode Antinode
Antinode

Node
Node
Node

FIGURE 3–22. A and B. Examples of modes of vibra-
tion that would occur in tubes. A. The wave patterns
for a tube open on both ends, called a half-wave reso-
nator. A half-wave resonator can produce harmonics
at integer multiples of the fundamental mode. B. The
wave patterns in a tube open only on one end, called a
quarter-wave resonator. A quarter-wave resonator can
produce harmonics at odd multiples of the fundamental
mode.

Node

Node Node

Node

Node Node

Node
Node

Antinode
Antinode Antinode

Antinode Antinode Antinode

FIGURE 3–21. A–C. Examples of modes of vibration
that would occur in a string that is attached at both
ends showing the rst mode or fundamental frequency
(A), the second mode or second harmonic (B), and the
third mode or third harmonic (C). Additional modes
can occur at integer multiples of the rst mode. At the
nodes, the displacement is zero and creates a standing
wave.

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3. PRoPERTIES oF SoUnD 43

ACOUSTICS OF SPEECH

The primary means of producing speech is
through air-flow supplied from the lungs, which
passes through the vocal structures of the larynx
and the oral and nasal cavities. The positioning
and movements of the articulators (tongue, lips,
velum, and jaws) alter the shape of the vocal
path that results in specific resonance patterns of
frequencies, amplitudes, and timing. The speech
sounds are propagated into the environment, re-
ceived, and ideally perceived by a listener. For
example, what acoustic parameters are neces-
sary for the listener to decide that they heard the
sound /d/ in the word day? Or how does one
perceive the word day differently than the words
die or bay? Also, in today’s world, human speech
can be synthesized and digitally generated by
a computer, largely based on what is known
about the meaningful acoustic characteristics of
the speech. Although the acoustic parameters of
speech are important, keep in mind that com-
munication involves much more than the simple
production, recognition, and perception of the
acoustic properties of speech.

Speech sounds can be classified into differ-
ent types. On the most basic level, there are vow-

els, which are mostly complex periodic sounds,
and consonants, which can be either complex pe-
riodic (with vocal fold vibration) or aperiodic vi-
brations (without vocal fold vibration). Table 3–4
lists the labels used to describe different types of
sounds. When the vocal folds vibrate, there is a
complex periodicity to the sound, called a voiced
sound. When the vocal folds do not vibrate, the
sound is aperiodic and called a voiceless sound.
Vowels are voiced, but consonants can be either
voiced or unvoiced. The normal average intensity
level of ongoing connected speech is about 65 to
75 dB SPL (Killion & Mueller, 2010; Thibodeau,
2007), and this “volume” is primarily carried by
the vowels. Consonants have less energy than the
vowels during connected speech, and contrib-
ute the most to word intelligibility. Figure 3–23
shows how conversational-level speech sounds
are distributed across the frequency and inten-
sity scales. This general distribution of speech
sounds is often referred to as the speech banana
due to its general outline encompassing ranges
of the vowels and consonants during ongoing
speech. As you can see in Figure 3–23, there is
as much as a 30 dB SPL difference between the
loudest vowel ( /u/) and the softest consonant
( /th/). Notice also that the vowels tend to be

TABLE 3–4. Labels Used to Describe Different Types of Sounds Related to the Place of Articulation

Manner of
Articulation Voicinga Bilabial Labio-dental Lingua-dental Alveolar Palatal Velar Glottal

Plosives (Stops) –
+

p(pea)
b(bee)

t(tea)
d(d id)

k(kit)
g(go)

Fricatives –
+

f(f in)
v(v ine)

θ(thin)
ð(the)

s(so)
z(zoo)

ʃ(she)
ʒ(luge)

h(he)

Affricates –
+

tʃ(chin)
dʒ( jot)

nasals –
+ m(me) n(no) ŋ(bang)

Liquids –
+

l(let)
r(red)

Glides –
+ w(we)

ʍ(whet)
j(yet)

aSome consonants are produced without voicing (–), and some are produced with voicing (+).

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AUDIOLOGY: SCIENCE TO PRACTICE44

lower in frequency, whereas many of the aperi-
odic noise-like consonants, called fricatives, are
higher in frequency.

In the following sections, only the very ba-
sics of the acoustic properties of the different
types of speech sounds are given, primarily their
frequency components; however, keep in mind
that amplitude and timing variations are also im-
portant acoustic properties of speech. In Chap-
ter 8 of this textbook, you will learn about the
clinical speech tests that are used to assess how
well a patient is able to recognize words and sen-
tences, and how a patient’s speech recognition
is altered by various disorders of the auditory
system. For a more in-depth understanding of
speech production, speech acoustics, and speech
perception, the interested reader is referred to
other sources, such as (Kent & Read, 2002; Ra-
fael, Borden, & Harris, 2007).

Spectrogram

Speech is composed of basic periodic and ape-
riodic vibrations that occur in relatively short
time periods, and is interspersed with short si-
lent periods between sounds. The frequency, am-

plitude, and time characteristics of speech can
be analyzed with some basic equipment. One of
the most important pieces of equipment used to
analyze speech sounds is a spectrograph, which
measures the spectra of speech sounds, words,
or sentences (in a relatively short time window)
recorded through a microphone. A spectrogram
is the graphical output from a spectrograph for
a specifi c speech utterance. A spectrogram dis-
plays frequency (along the y-axis) as a function
of time (along the x-axis). The amplitudes of the
different frequencies are also represented in a
spectrogram by the relative darkness of the fre-
quency bands, that is, the more intense frequen-
cies are seen as darker bands. Figure 3–24 shows
examples of spectrograms for some vowels and
consonants. As you can see in Figure 3–24A, the

Frequency (Hz)

100 1000 10000

dB
S

ou
nd

P
re

ss
ur

e
Le

ve
l

0
10
20
30
40
50
60
70
80
90
100

110

120

Frequency (Hz)
100 1000 10000

dB
S
ou
nd
P
re
ss
ur
e
Le

ve
l (

dB
S

P
L)

0
10
20
30
40
50
60
70
80
90

100
110
120

Vowels F1

1st peak voiced
fricatives and nasals Voiceless

fricatives

2nd peak voiced
fricatives and

nasals

Vowels F2

FIGURE 3–23. General distribution of speech sounds
during normal conversational level of connected speech.
The overall level of conversational speech is about 65 dB
SPL. The outer most outlined area is called the speech
banana.

F
re

qu
en

(k
H

5
4
3
2
1

A
m
pl
itu

A
m
pl
itu
de

5
4
3
2
1 F

re
qu

en
cy

H
z)

i a u

a f a a v a

5
4
3
2
1 F
re
qu
en
cy

(k
H
z)

Time

A
m
pl
itu
de

a s a a z a

A
B

FIGURE 3–24. A and B. Spectrographic recordings
for three different vowels in isolation (A), and some
voiceless and voiced fricatives (B).

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3. PRoPERTIES oF SoUnD 45

vowels show three or four darker frequency re-
gions (bands). These darker frequency bands are
called formants, beginning with the first formant
(F1), the next higher F2, and so forth. Formants
vary depending on the resonance properties as-
sociated with the positions of the articulators,
and are similar to those harmonics seen with the
example of the quarter-wave resonator. Vowels
behave more like the complex periodic vibra-
tions that we saw in the preceding section. Other
speech sounds may be aperiodic, like the /s/
shown in Figure 3–24B, which does not have the
discrete frequency bands like those seen with
vowels, but instead shows a wider range of fre-
quencies as expected with a noise-type sound.
The following sections give a brief overview of
the acoustics properties for the various vowel-
like speech sounds and the various noise-like
speech sounds. Although not covered in this text,
keep in mind that there are also corresponding
amplitude variations associated with connected
speech, as well as important temporal factors
such as duration of sounds and silent intervals.

Vowels

Vowels carry most of the audible energy in
speech, and generally have lower frequencies
and higher intensities than consonants. Vowels
are complex periodic vibrations (voiced) that re-
sult from the vibration of the vocal folds. The
frequency of vocal fold vibration is the funda-
mental frequency (f0) which gives the sound its
perceived pitch, and can vary depending on the
vowel as well as the size of the larynx (which
relates to males generally having a lower sound-
ing voice). As described earlier, vowels can be
characterized by their F1 and F2. In general, the
F1 varies inversely with the height of the tongue,
and F2 varies with the forward/backward posi-
tion of the tongue. For example, /i/ is produced
with the tongue in its highest position and most
forward in the mouth, whereas /a/ is produced
with the tongue in its lowest position and as far
back as possible. Lip rounding is done for some
back and center vowels and its effect is to ex-
tend the vocal tract and thus lower all formant
frequencies. Keep in mind that the formant fre-

quencies are not precise numbers, but are best
considered as elliptical regions that vary depend-
ing on the speaker due to variations in size of
vocal tract, articulators, and dialect. Figure 3–25
shows how the different vowels can be sepa-
rated into their F1 and F2 elliptical areas, and be
relatively distinct from each other.

During speech, vowels can also vary by their
duration. For example, some vowels are longer
in duration, like those in open syllables (e.g.,
“see” “so”), whereas others are shorter in dura-
tion like those in closed syllables (e.g., “sit” “sat”).
Additionally, vowels that are produced in con-
text with other consonants also have a dynamic
shifting of their formant frequencies, called for-
mant transitions, where there may be a rising
or falling frequency transition depending on the
preceding and/or target consonant. Combining
vowel sounds, called semivowels or diphthongs,
are characterized by formant transitions, and the
shifts in F2 are the most distinguishing charac-
teristic used to identify different semivowels and
diphthongs.

Consonants

Consonants are considered the sounds that con-
tribute most toward intelligibility as they precede
and/or follow vowels to define words or parts of
words. The acoustic properties of consonants are

F1 (kHz)

1.0
2.0
4.0

0 0.4 0.8 1 2

F
2

(
k
H

z
)

heard

h
e
e
d

h
id

h
e
a
d

ha
d

hu
d

w
h
o
̕d

h
o
o
d ho

ha
w
ed

i
æ

ɑЗ

FIGURE 3–25. Distribution of F1 and F2 formants for
English vowels for a variety of speakers. Source: From
Kent and Read, 2002, p. 170, with permission of the
authors.

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AUDIOLOGY: SCIENCE TO PRACTICE46

a bit more complicated than vowels, and one is
not able to give as general a description as we
were able to do with the formant structure of
vowels. Consonants are divided into several dif-
ferent types. Some consonants are voiced, some
have a noise quality, some only have a period of
silence, and some may involve the nasal cavity.
Only a brief description of these characteristics
is given here, and only some selective examples
are shown on a spectrogram. With some prac-
tice, you may be able to recognize the patterns of
vowels and consonants in the complete sentence
“The sunlight strikes raindrops in the air,” shown
in Figure 3–26.

Stops (or plosives) are produced by a brief
period in which the airflow is blocked. The
blockages can occur at the lips, alveolar area, or
velum, and are referred to as bilabial, alveolar,
or velar stop. Stops can be voiced or unvoiced
depending on if the vocal folds are set into vibra-
tion. During the closure, air pressure is built up
and when the stop is opened, there is a burst of
air flow. Fricatives are noise-like sounds that are
produced by passing air through the oral cavity
in which the articulators are positioned in a way
to create turbulence in the airflow. The different
fricatives are produced by the location (place) of
constriction from the most forward point of the
oral cavity at the lips to the rearmost position at
the glottal area. Fricatives can be voiced (e.g., /v/ )
or unvoiced (e.g., /f/ ) at the same place of articu-
lation. Affricates are created by the transition of

a stop into a fricative. With nasals, the velopha-
ryngeal port is opened so that sound energy can
pass through both the nasal and oral tracts or
through only the nasal tract. The formants of the
nasals depend on the length of the cavity from
the uvula to the nostrils, and are voiced with the
vibration of the vocal folds.

FILTERING

Filtering is a means by which certain frequencies
are excluded and certain frequencies are allowed
to pass. Filtering can be used to generate a sound
that is composed of a specified range of frequen-
cies by filtering out some portion of a wider range
of frequencies. For example, one can start with
white noise and then filter out some of the fre-
quencies so that a more restricted range of fre-
quencies is passed.

Figure 3–27 shows the spectra for different
types of commonly used filters. The band of fre-
quencies that is passed is represented under the
curve, and those outside the curve are the fre-
quencies that are filtered out. The point where
frequencies begin to be filtered out is called the
cutoff frequency and is usually defined at the
point that is 3 dB less than the peak (called 3 dB
down-points or half-power point). The extent
to which the frequencies are excluded is deter-
mined by the slope of the curve, called atten-
uation rate or rejection rate, which is usually

F
re
qu
en

cy
(k

H
z)

m
pl

itu
de

5
4
3
2
1

ð s ʌ n l ᾱĪ t s t r ᾱĪ ks rēĪn drα p s I n ð i Ԑ r

FIGURE 3–26. Sample waveform and spectrogram of the sentence, “The
sunlight strikes raindrops in the air.”

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3. PRoPERTIES oF SoUnD 47

specified in dB per octave (dB/octave). An octave
means a doubling or halving of the frequency.
As an example (see Figure 3–27A), a high-pass
filter passes frequencies higher than the cutoff
frequency and rejects frequencies lower than the
cutoff frequency at a specified dB/octave slope
toward the lower frequencies. In this example,
the filter would be called a high-pass filter with
a 2000 Hz low frequency cutoff and a rejection
rate of 10 dB/octave. The other examples in Fig-
ure 3–27 include a low-pass filter that passes all
the frequencies lower than the cutoff frequency
and rejects frequencies higher than the cutoff
frequency at a specified dB/octave slope directed
toward the higher frequencies. A band-pass filter
passes a band of frequencies as defined by the
high and low cutoff frequencies and rejects fre-

quencies above and below the cutoff at the spec-
ified rejection rates toward the higher and lower
frequencies. The band-reject filter (also known
as a notched filter) specifies a range of frequen-
cies in the middle of a wider range of noise that
is rejected, and the frequencies on both sides of
the specified band-reject area are passed.

A special type of band-pass filtered noise is
called narrowband noise, where there is a rela-
tively restricted range of frequencies. These fre-
quencies are often described by the width of the
curve as measured across the 3 dB down points
from the center frequency. A commonly used nar-
rowband noise is called a one-third octave nar-
rowband noise, which means the filter is one third
of an octave wide at the 3 dB down points. Fig-
ure 3–28 shows the spectra for some one-third

Frequency (kHz)

A
tte

nu
at

io
n

(d
B
)

-50

-40

-30

-20

-10

.25 1 2 4 8.50 16

Frequency (kHz)
A
tte
nu
at
io
n
(d
B
)
-50
-40
-30
-20
-10
0

.25 1 2 4 8.50 16
Frequency (kHz)

A
tte
nu
at
io
n
(d
B
)
-50
-40
-30
-20
-10
0
.25 1 2 4 8.50 16
Frequency (kHz)
A
tte
nu
at
io
n
(d
B

)
-50

-40
-30
-20
-10
0
.25 1 2 4 8.50 16

10 dB/octave

3 dB down

LF cut-off

HF cut-off

High Pass

Low Pass

Band Pass

LF cut-off HF cut-off

Band Reject

LF cut-off HF cut-off

30 dB/octave

A
B
C

FIGURE 3–27. A–D. Examples of different types of lters. The
region under the curves shows those frequencies that are heard
(passed). The places where the lter begins to reject frequencies
are called cutoff frequencies, which are at the 3 dB down points.
The lter’s rate of frequency rejection is indicated by the dB/octave.
A. Highpass lter with 2000 Hz cutoff with 10 dB/octave rejection
rate. B. Lowpass lter with 2000 Hz cutoff with 10 dB/octave rejec-
tion rate. C. Bandpass lter with 1000 Hz low frequency cutoff and
4000 Hz high frequency cutoff, with 10 dB/octave rejection rates.
D. Bandreject lter with 1000 and 4000 Hz cutoff points, with 30 dB/
octave rejection rates.

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AUDIOLOGY: SCIENCE TO PRACTICE48

SYNOPSIS 3–3

l Humans are capable of hearing sounds from 20 to 20,000 Hz; however, we
are most sensitive to frequencies in the 500 to 2000 Hz range, and it takes
slightly greater amounts of sound pressure (or intensity) for lower and higher
frequencies to be just audible (threshold). The variation threshold as a function
of frequency is referred to as the threshold of audibility curve.

l The wavelength of a sound (λ) describes how far a pure tone travels in one
cycle. The wavelength can be calculated by the equation λ = c/f, where c is the
speed of sound and f is the frequency. Conversely, if you know the wavelength,
the frequency can be calculated from f = c/λ.

l Complex sounds are much more typical in our environment than pure tones;
however, any complex sound is the result of some combination of pure
tones with specic amplitudes and starting phases. The individual sinusoidal
components of complex sounds can be determined using equipment that can
perform a fast Fourier transform (FFT).

l A spectrum describes a sound’s amplitude or starting phase (along the y-axis)
as a function of frequency (along the x-axis). A line spectrum is used when
discrete (and usually limited) frequencies contribute to the complex vibration.
A continuous spectrum is used when a range of frequencies (all inclusive)
contributes to the complex vibration.

l A periodic vibration repeats itself at regular time intervals. Complex vibrations
can be periodic if the combined waveform repeats itself over time; periodic
complex vibrations occur when the combined pure tones are harmonically
related as integer multiples of the lowest frequency, called the fundamental

Frequency (kHz)
A
tte
nu
at
io
n
(d
B
)

-15

-12

-9
-6
-3
0
.25 1 2 4 8.50 16

Frequency (kHz)

A
tte
nu
at
io
n
(d
B
)
-15
-12
-9
-6
-3
0
.25 1 2 4 8.50 16

1 kHz NB Noise
(1/3 octave wide)

12 dB/octave

B 1 kHz NB Noise
(1/3 octave wide) .5 1 2 4

NB Noises (CF in kHz)

FIGURE 3–28. A and B. Spectra for some one-third octave narrowband noises. A. The
width of the lter is described by how wide the spectrum is at the 3 dB down points from the
center frequency, with the corresponding dB/octave rejection rates. B. Some narrowband
noises, centered at 0.5, 1, 2, and 4 kHz that are commonly used in audiology.

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3. PRoPERTIES oF SoUnD 49

octave narrowband noises. Narrowband noises
are used frequently as noise maskers during
basic hearing tests. Filtering can also be used
when analyzing or measuring a complex wave
pattern to exclude frequencies that you are not
interested in analyzing or measuring, and instead
focuses only on those frequencies that are of in-
terest. This type of filtering is used in many of

the physiological measures from the auditory
system.

PSYCHOACOUSTICS

The study of how humans perceive the acous-
tic properties of sound is called psychoacoustics.

SYNOPSIS 3–3 (continued )

frequency (f0). A sawtooth waveform results when all harmonics (1f0 + 2f0 + 3f0 +
4f0 . . .) are included and a square wave results when only the odd harmonics
(1f0 + 3f0 + 5f0 + 7f0 . . .) are included.

l An aperiodic complex vibration (often called noise) does not repeat itself at
regular time intervals and typically results from a range of pure tones with
random starting phases. White noise (analogous to white light) has an innite
number of frequencies present with random phases.

l Most vibrating objects (except for a pure tone), including air molecules in tubes,
have a fundamental frequency and additional harmonics. The vocal tract and
ear canal are similar to a tube that is open at one end, called a quarter-wave
resonator. A quarter-wave resonator produces vibrations at a fundamental
frequency and at odd integer harmonics. The resonance frequencies are
dependent on the wavelengths associated with the length of the tube.

l Speech has specic acoustic properties generated by airow passing through
the vocal fold, oral cavity, and nasal cavity, resulting in complex periodic and
aperiodic acoustic waveforms. The articulators modify the airow depending on
the targeted speech sound.

l Vowels are more intense than consonants in connected speech and produce
the perception of voice loudness. The long-term average level of conversational
speech is about 65 dB SPL.

l Vowels are complex periodic vibrations with a fundamental frequency (giving
rise to the pitch of the voice), and additional bands of energy called formants.
The F1 and F2 formants are most important for vowel differentiation.

l Consonants can be periodic if accompanied by vocal fold vibration (voicing) or
aperiodic if entirely noise-like (unvoiced). There are many types of consonants
depending on the manner and place of articulation. Consonants are generally
less intense than vowels and contribute most to intelligibility when in connected
speech.

l Filtering is a way to exclude certain frequencies and allow other frequencies to
pass through. Filters are used to shape the spectra of noise stimuli and/or to
focus on a specic frequency range that is to be analyzed. Common types of
lters include highpass, lowpass, bandpass, and bandreject as dened by their
cutoff frequencies and rejection rates. narrowband noises, used extensively in
hearing testing, are ltered noises that are typically onethird of an octave wide.

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AUDIOLOGY: SCIENCE TO PRACTICE50

The following sections will present basic infor-
mation on how frequency and intensity translate
into our perception of loudness and pitch; how
our thresholds change as the duration of a sound
is shortened, called temporal integration; and, fi-
nally, how we use acoustic information to deter-
mine where sounds are coming from, called local-
ization. The introductory material covered in this
chapter only touches the surface of this fascinat-
ing area and only covers how normal hearing hu-
mans perceive simple sounds. For more advanced
coverage of this topic for a variety of simple and
complex sounds, the interested reader is referred
to other texts (Durrant & Lovrinic, 1995; Gelfand,
2009; Moore, 2013; Zwicker & Fastl, 2013).

Loudness

Loudness is generally considered the psycholog-
ical correlate of intensity. Most of us have a gen-
eral idea that soft and loud sounds are related to
low and high intensities (or pressures) of sounds.
As discussed earlier, the ear responds to a wide
range of intensities (or pressures); the minimum
level is perceived as threshold and the upper
limit is perceived as being uncomfortably loud.
As we learned from the threshold of audibility
curve, it takes a different amount of intensity to
reach threshold for different frequencies. So, an
obvious question is what intensities are needed
to maintain equal loudness across frequencies?
To answer this question, a loudness-matching
procedure is typically used in which the dB SPL
for different frequencies are adjusted until they
sound equally loud to a 1000 Hz reference tone
(Fletcher & Munson, 1933; Robinson & Dadson,
1956). The scaling unit used to compare loudness
across frequencies is called a phon. Figure 3–29
shows a series of phon curves. The phon equates
loudness across frequencies (also called equal
loudness contours). The level of each phon curve
is defined as the dB SPL of a given level of a
1000 Hz tone. For example, a loudness level of
30 phons is equal to a 1000 Hz tone presented at
30 dB SPL, and a loudness level of 60 phons is
equal to a 1000 Hz tone presented at 60 dB SPL.
Different phon curves are established for differ-

ent levels of the 1000 Hz reference tone. The
dB SPLs needed for other frequencies to sound
equally loud to the 1000 Hz tone, at a specified
phon level, are measured to establish the corre-
sponding phon curve across the frequency range.
In other words, all frequencies at the given phon
level (along the same phon curve) are judged to
be equally loud even though their actual SPLs
are different. As you can see from Figure 3–29,
the general shape of the phon curves follows
the threshold of audibility curve; however, they
tend to flatten out across frequency as the phon
level increases, especially in the lower frequen-
cies. This means that at higher sound levels it
does not take as much increase in dB SPL in the
lower frequencies to sound equally loud to the
mid frequencies.

The phon scale does not tell us much about
how our perception of loudness is related to the
continuum of sound pressures. Another question
of interest is how does a scale of loudness re-
late to a range of sound pressures? For example,
if the dB SPL of a sound is doubled, does the

FIGURE 3–29. Phon scales of loudness (or equal
loudness contours). A phon is dened as the loudness
associated with a 1000 Hz reference tone. Each line
represents frequencies that are perceived as equally
loud for the given phon level. Source: From Yost, 2013,
p. 190. Copyright 2013 by Koninklijke Brill.

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3. PRoPERTIES oF SoUnD 51

perceived loudness also double? Or how much
increase in dB SPL is needed to achieve a dou-
bling of the perceived loudness? The relationship
of loudness to pressure (or intensity) is gener-
ally determined by using magnitude estimation
or scaling method (Stevens, 1956). This type of
loudness scale uses sones as the unit of loudness,
where one sone is defined as the loudness of a
1000 Hz tone at 40 dB SPL. In these types of ex-
periments, the subject is asked to adjust the dB
SPL of the tone until the loudness is judged to be
half, double, triple, and so on, of the loudness of
the reference value. In other words, how many
dB SPL corresponds to 2 sones or 0.5 sones? The
data are typically presented for a 1000 Hz tone;
however, similar data can be obtained for differ-
ent frequencies by making the reference value
equal to the loudness in phons for the frequency
being measured. Figure 3–30 shows the relation-
ship that occurs between the loudness in sones
and the dB SPL of a 1000 Hz tone (or loudness
level in phons). As you can see, the sone scale
for loudness (on a log-log plot) shows a rela-
tively straight line above 30 dB SPL for a 1000 Hz
tone. In this region, a doubling of loudness cor-
responds to a 10 dB increase in sound pressure
and approximates a power function, where the
slope of the line is the exponent of the power
function; in this case, loudness = pressure6. For

levels between threshold and 30 dB SPL, the
loudness function is much steeper and does not
fit the simple power function. Notice also that
the entire range of sound pressures (107) is com-
pressed into a range of only around 100 sones.

Pitch

Pitch is generally considered the psychological
correlate of frequency. Most of us have a sense
that low and high-pitch sounds are related to low
and high frequencies. Although we can detect a
wide range of frequencies and can attribute a
general perception of pitch to these frequencies,
the question of interest here is how does a scale
of pitch relate to a scale of frequency, that is, if
we double the frequency of a sound, does the
pitch also double? In other words, how much of
a frequency increase is needed for a doubling of
the perceived pitch? As you will see, there is not
a one-to-one correspondence between pitch and
frequency. The relationship of pitch to frequency
was first described by Stevens and Volkmann
(1940). The pitch scale is typically presented in
units called mels. The mel scale assigns a stan-
dard reference value of 1000 mels to the pitch as-
sociated with 1000 Hz. The subject then adjusts
the frequency of a tone until the pitch is judged
to be half, double, triple, and so on, of the pitch
of the 1000 Hz reference tone. In other words,
what frequency best corresponds to 500, 2000,
or 3000 mels? Figure 3–31 shows the relationship
that occurs between pitch (linear scale) and fre-
quency (logarithmic scale). As you can see, the
mel scale for pitch does not show a one-to-one
relation to frequency. For example, a doubling of
frequency from 1000 to 2000 Hz corresponds to
a 1.5 increase in pitch (from 1000 to 1500 mels).
Conversely, a doubling of pitch from 1000 to
2000 mels corresponds to about a threefold in-
crease in frequency (from 1000 to 3000 Hz). No-
tice also that the entire range of frequencies (20
to 20,000 Hz) is compressed into a range of only
3500 mels, and that the data follow a curvilinear
function in a semi-log plot across the frequency
range.

Pitch also changes with intensity, as shown in
Figure 3–32, for a variety of frequencies (Stevens,

dB Sound Pressure Level

0 10 20 30 40 50 60 70 80 90 100

S
on

0.01

0.10

1.00

10.00

100.00

1000 Hz

FIGURE 3–30. Sone scale of loudness for 1000 Hz.
one sone equals the loudness associated with a 1000 Hz
tone at 40 dB SPL. A doubling of loudness occurs for
tenfold increases in stimulus level.

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AUDIOLOGY: SCIENCE TO PRACTICE52

1935). These pitch versus intensity data are
called equal pitch contours. In general, increas-
ing intensity results in an increased pitch for the
higher frequencies and a decreased pitch for the
lower frequencies (Durrant & Lovrinic, 1995; Gu-
lick, Gescheider, & Frisina, 1989). It should be
pointed out that these increases and decreases
in pitch with intensity are relatively small and
not generally noticeable except under controlled
laboratory conditions (Cohen, 1961).

Temporal Integration

Temporal integration describes how the thresh-
old of audibility for a sound changes with the du-
ration of the sound. In general, as the duration of
a sound is shortened to less than 200 ms, the level
of the sound must be increased in order for the
sound to be audible (Durrant & Lovrinic, 1995;
Watson & Gengel, 1969). Figure 3–33 shows how
the threshold changes as a function of duration.
As you can see, there is about a 10 dB increase
in level (threshold shift) for a tenfold decrease
in duration. In other words, as the duration is
shortened from 200 to 20 ms, the sound level
must be increased by 10 dB to remain audible.
Similarly, as the duration is shortened from 20 to
2 ms, an additional 10 dB increase in the level of
the sound is needed to remain audible. It should

also be pointed out that for tones less than 10 ms
in duration, the quality of the sound also changes
significantly, such that the tonality is lost and it is
perceived as a brief click (transient) type sound.
These brief transients also spread their energy
across a wider frequency range called spectral
splatter. You can also see from Figure 3–33 that
for sounds with durations greater than 200 ms,
the threshold remains constant.

Localization

Localization refers to the ability to determine the
direction from which a sound is coming. In gen-

150 (220)

(400)

(1000)
500 (700)

300

1K
2K (1600)
3K (2000)

4K (2300)

5K (2500)

8K (2900)

30 40 50 60 70 80 90 100 110 120

2 %

SOUND LEVEL (dB)

Δ
F

f
o

r
C

N
S

T
P

IT
C

(
%

F
)

FIGURE 3–32. Equal pitch contours. Each line repre-
sents equal pitch as stimulus level increases. For lower
frequencies, as stimulus level is increased, the fre-
quency tends to decrease. For higher frequencies, as
stimulus level is increased, the frequency tends to in-
crease. Source: From Durrant and Lovrinic, 1995, p. 279.
Copyright 1995 by Williams and Wilkins.

Frequency (Hz)
100 1000 10000

M
el

s
0

1000

2000

3000

4000

FIGURE 3–31. Mel scale of pitch. The pitch associated
with 1000 Hz is dened as 1000 mels. The range of
audible frequencies (20 to 20,000 Hz) is compressed
into about 3500 mels.

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3. PRoPERTIES oF SoUnD 53

eral, our ability to localize is greatly dependent
on the use of both ears, called binaural hearing.
Most animals have a keen sense of localization,
and many animals are able to move their pin-
nae to help them localize. Humans, on the other
hand, do not move their auricles as a means of
localizing. Instead, humans rely (unconsciously)
on different arrival times and/or intensities of
sounds at the two ears to determine from where
sounds are coming. These mechanisms are re-
ferred to as interaural time differences or inter-
aural intensity differences. These two mecha-
nisms can explain localization of simple sounds
that come from one side of the head. For local-
ization, clearly two ears are better than one, and
a typical complaint of people with hearing loss
in one ear is that they have some difficulty local-
izing sounds.

Figure 3–34 shows how interaural time and
interaural intensity mechanisms operate when
listening with two ears to a sound presented to
one side of the head. As shown in Figure 3–34B,
higher frequencies (>1500 Hz) have shorter
wavelengths as compared to the size of the head,
and these frequencies tend to be blocked by the
head (Fedderson, Sandel, Teas, & Jeffress, 1957).
In this case, the sound at the ear farther away

from the sound source is less audible, called
head shadow. For lower frequencies, shown in
Figure 3-34C, the wavelength is larger than the
size of the head and wraps around the head
due to diffraction and does not create interau-
ral intensity differences; however, it does take
slightly more time for the sound to get to the
ear farther away from the sound source. These
interaural time differences appear to be impor-
tant for lower frequency localization as long as

2 20 200 2000

0
10
20
30
40

Duration (ms)

10 fold

10 dB

dB
s

hi
ft

re
la

tiv
e

to
s

te
ad

y
st

at
e

FIGURE 3–33. Temporal integration function. This
shows how the threshold for a pure tone changes as a
function of duration. As the duration is shortened by a
factor of 10 (e.g., from 200 to 20 ms), the sound level
must be increased by 10 dB to remain audible.

>
A

B
>

>
C

FIGURE 3–34. A–C. Illustrations showing factors
important for sound localization in the horizontal
plane. A. Interaural time differences between the two
ears; varies as a function of azimuth. B. Interaural
intensity differences between the two ears resulting
from sound shadow area that occurs at the ear farther
away from the sound source when wavelength is
short, which may explain some localization at high
frequencies. C. Sound shadow does not occur when
wavelength is at least as long as the width of the head.

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AUDIOLOGY: SCIENCE TO PRACTICE54

the wavelength is larger than the distance be-
tween the two ears; however, this simple model
has been shown to have some discrepancies in
more recent studies (Kuhn, 1977) and these are
beyond the scope of this textbook. As the direc-
tion of the sound source moves more toward the
center, localization based on interaural time and
intensity differences becomes more difficult. In
those situations, and in vertically directed local-
ization, spectral differences in the sound from

front to back, due to the shape of the auricle,
may help with localization at higher frequen-
cies because the wavelengths are smaller than
the auricle (Durrant & Lovrinic, 1995). In the
real world, humans are able to move their heads
and/or use visual cues to help them identify the
source of a sound; and while listeners with uni-
lateral hearing loss have some localization dif-
ficulty, they are able to localize to some degree
by using these other cues.

SYNOPSIS 3–4

l Psychoacoustics is the study of how we perceive the different acoustic
properties of sound; loudness is the perceptual correlate of intensity and pitch
is the perceptual correlate of frequency.

l The phon scale equates loudness across frequencies (also called equal loudness
contours), as matched to the dB SPL of a 1000 Hz tone: For example, a 40 dB
phon curve equates the loudness across frequencies to a 1000 Hz tone at
40 dB SPL.

l The sone scale describes how perceived loudness of a tone relates to changes
in its change in dB SPL. One sone equals the loudness of a 40 dB SPL 1000 Hz
tone (also 40 phons). For 1000 Hz above 30 dB SPL, an increase of 10 dB SPL
results in a doubling in loudness, and is described as a power function. The
range of audible SPLs is compressed into a range of only about 100 sones.

l The mel scale describes how changes in pitch correspond to changes in
frequency. The mel scale is based on the pitch of 1000 Hz = 1000 mels. The
mel scale shows less of an increase in perceived pitch for a corresponding
increase in frequency. The entire range of audible frequencies is compressed
into only about 3500 mels.

l Equal pitch contours describe how pitch of a specic tone changes as a function
of intensity. Although the effects are quite small, increasing the intensity of
high frequencies causes the pitch to increase; increasing the intensity of low
frequencies causes the pitch to decrease.

l Temporal integration relates a tone’s threshold to changes in the tone’s
duration. There is about a 10 dB increase in threshold for each tenfold decrease
in duration below 200 ms (e.g., 200 to 20 ms). For durations longer than 200 ms,
threshold remains constant (complete integration).

l Localization of a sound’s source is easiest with binaural hearing. Localizing
the source of a sound from the sides is facilitated by the interaural intensity
differences for higher frequencies (due to head shadow effect), and interaural
time differences for lower frequencies. Localizing from front/back and in the
vertical plane are facilitated by spectral differences due to the auricle.

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3. PRoPERTIES oF SoUnD 55

REFERENCES

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Cohen, A. (1961). Further investigations of the effects
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Durrant, J. D., & Lovrinic, J. H. (1995). Bases of Hear-
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Fedderson, W. E., Sandel, T. T., Teas, D. C., & Jeffress,
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Fletcher, H., & Munson, W. A. (1933). Loudness, its
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Kent, R. D., & Read, C. (2002). Acoustic Analysis of
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Killion, M. C., & Mueller, H. G. (2010). Twenty years
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Kramer, S. J., & Small, L. (2019). Audiology Workbook.
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Kuhn, G. F. (1977). Model for the interaural time dif-
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Moore, B. C. J. (2013). Introduction to the Psychology
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Mullin, W. J., Gerace, W. L., Mestre, J. P., & Velleman,
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Stevens, S. S. (1935). The relation of pitch to inten-
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