Table 17.3
Sample Binar
Number in
1
2
3
10
37
275
The binary numbers read from the CD are converted back to voltages,
and the waveform is reconstructed, as shown in Figure 17.15. Because the
sampling rate is so high44 100 voltage readings each secondthe f

516
C HAPTE R 17 Sound Waves
Derivation
Equation 17.3
of
Consider a thin disk-shaped element of gas whose circular cross section is
parallel to the piston in Figure 17.2. This element will undergo changes in
position, pressure, and density as a sound wave

S E C T ION 17. 3 Intensity of Periodic Sound
Waves
517
The piston transmits energy to this element of air in the tube, and the
energy is propagated away from the piston by the sound wave. To evaluate
the rate of energy transfer for the sound wave, we sha

S E C T ION 17. 2 Periodic Sound Waves
17.2
515
Periodic Sound Waves
This section will help you better comprehend the nature of sound waves. An
important fact for understanding how our ears work is that pressure variations
control what we hear.
One can pr

514
C HAPTE R 17 Sound Waves
Table
17.1
Section 12.4) and density !, the speed of sound waves in that
medium is
(17.1)
Speed of Sound in
Various
Media
Medium
(m/s)
v
Gases
Hydrogen (0C)
286
1
Helium (0C)
972
Air (20C)
343
Air (0C)
331
Oxygen (0C)
317
1
90

Problems
what factor? This phenomenon led to the collapse of
part of the Nimitz Freeway in Oakland, California,
during the Loma Prieta earthquake of 1989.
Section 16.6
tion corresponding to their
being seated and
maximum position corresponding to their st

Answers to Quick Quizzes
of the string to the other. Give your result as a
multiple of ,t0
! L/v0.
67. A pulse traveling along a string of linear mass density
+ is described by the wave function
y ! [A0e"bx]
sin(kx " 't)
where the factor in brackets befor

508
C HAPTE R 1 6 Wave Motion
distance equal to three fourths of the length of the
string (Fig. P16.30). An object of mass m is suspended
from the center of the string, putting a tension
in
the
string. (a) Find an expression for the
transverse wave speed

510
C HAPTE R 1 6 Wave Motion
point. (a) Determine the tension in the cord when the
block is at this lowest point. (b) What is the length of
the cord in this stretched position? (c) Find the
speed of a transverse wave in the cord if the block is
held in t

Problems
where k ! 3.10 rad/cm and ' ! 9.30 rad/s. How
far does a wave crest move in 10.0 s? Does it move in
the positive or negative x direction?
11. Consider further the string shown in Figure 16.10
and treated in Example 16.3. Calculate (a) the
maximum

506
C HAPTE R 1 6 Wave Motion
string is doubled, by what factor does the
amplitude change? Does the wave speed change
under these circum- stances?
8. Consider a wave traveling on a taut rope. What is the
dif- ference, if any, between the speed of the wave

Questions
S U M MAR Y
A transverse wave is one in which the elements of the medium move in a
direction perpendicular to the direction of propagation. An example is a wave on
a taut string. A longitudinal wave is one in which the elements of the medium
mov

S E C T ION 1 6 . 5 Rate of Energy Transfer by Sinusoidal Waves on
Strings
501
According to Equation 16.18, the speed of a wave on a string increases as
the mass per unit length of the string decreases. In other words, a wave
travels more slowly on a heav

504
C HAPTE R 1 6 Wave Motion
The right side of this equation can be expressed in a different form if we note
that the partial derivative of any function is defined as
)f ,x : 0 f (x # ,x) "
)x
f (x)
% lim
,
x
and f(x) with ()y/)x )A, we see
If we associa

518
C HAPTE R 17 Sound Waves
amplitude 'Pmax;
in this case, we use
Equation 17.4 to obtain
(17.6
)
2
I#
'P v
2
Now consider a point source emitting sound waves equally in all
directions. From everyday experience, we know that the intensity of sound
decrea

S E C T ION 17. 3 Intensity of Periodic Sound
Waves
519
Quick Quiz 17.4
A vibrating guitar string makes very little sound
if it is not mounted on the guitar. But if this vibrating string is attached to the
guitar body, so that the body of the guitar vibra

Chapter 17
Sound Waves
C HAP T E R O U T L I N E
17.1 Speed of Sound Waves
17.2 Periodic Sound Waves
17.3 Intensity of Periodic Sound
Waves
17.4 The Doppler Effect
17.5 Digital Sound Recording
17.6 Motion Picture Sound
Human ears have evolved to detect s

532
C HAPTE R 17 Sound Waves
Figure 17.15 The reconstruction of the sound wave sampled in Figure 17.13.
Notice that the reconstruction is step-wise, rather than the continuous
waveform in Figure 17.13.
Example 17.8
How Big Are the Pits?
In Example 10.2, w

S E C T ION 17. 5 Digital Sound Recording
Figure 17.12 An
Edison
phonograph.
Sound information is
recorded in a
groove on a
rotating cylinder
of wax. A needle
follows the groove
and vibrates
accord- ing to the
sound information. A diaphragm
and a
horn mak

530
C HAPTE R 17 Sound Waves
is the distance from the center. We first
find T:
T #1
#
1
!
(B) The linear speed at the inner edge is
# 0.030 min 60 s
f
33.33
rev/min
" # 1.8
s
1
min
2 r
v # in.) #
T
Now, the linear speed at the outer
edge is
2 (6.0
# 21 in

S E C T ION 17. 4 The Doppler Effect
Sol
utio
n
What If? While the subs are approaching each other,
(A) We use Equation 17.13 to find the Doppler-shifted
fre- quency. As the two submarines approach each
other, the ob- server in sub B hears the frequency
f

528
C HAPTE R 17 Sound Waves
Figure 17.11 The Vshaped bow wave of a
boat is formed because
the boat speed is
greater than the speed
of the water waves it
gener- ates. A bow wave
is analogous to a shock
wave formed by an
airplane traveling faster
than soun

524
C HAPTE R 17 Sound Waves
wavelength ( is unchanged. Hence, using Equation 16.12, v # (f, we can
say that the frequency f . heard by the observer is increased and is given by
f.# v.
v $ vO
#
Because ( # v/f, we can express f . as
f
(observer moving tow

S E C T ION 17. 4 The Doppler Effect
v
waves
(a)
v
v
w
av
es
boat
(b)
v
w
av
es
Figure 17.7 (a)
Waves mov- ing
toward a stationary
boat. The waves travel
to the left, and their
source is far to the
right of the boat, out
of the frame of the
photograph.
(b

Sound waves are
the most common example of longitudinal waves. They
travel through any material medium with a speed that depends on the
properties of the medium. As the waves travel through air, the elements of
air vibrate to produce changes in density an

526
C HAPTE R 17 Sound Waves
Example 17.5
The Broken Clock Radio
Your clock radio awakens you with a steady and irritating
and cannot be turned off. In frustration, you drop the clock
radio out of your fourth-story dorm window, 15.0 m from
the ground. Ass

S E C T ION 17. 4 The Doppler Effect
f. #
!
(source moving toward observer)
v
525
(17.11)
f
That is, the observed frequency is increased whenever the source is moving
toward the observer.
When the source moves away from a stationary observer, as is the ca

522
C HAPTE R 17 Sound Waves
boundary of the white area is straight, because the psychological response is
relatively independent of frequency at this high sound level.
The most dramatic change with frequency is in the lower left region of
the white area,

S E C T ION 17. 3 Intensity of Periodic Sound
Waves
521
machines in this example is to be doubled, how many
ma- chines must be running?
I2
log
I
# 1
Answer Using the rule of thumb, a doubling of
loud- ness corresponds to a sound level increase
of 10 dB. T