Fundamentals of Physics

David Halliday, Robert Resnick , Jearl Walker

Chapter 17

Waves-II - all with Video Answers

Educators

Chapter Questions

Problem 1

Two spectators at a soccer game see, and a moment later hear, the ball being kicked on the playing field. The time delay for spectator $A$ is 0.23 s, and for spectator $B$ it is 0.12 s. Sight lines from the two spectators to the player kicking the ball meet at an angle of $90^{\circ} .$ How far are (a) spectator $A$ and $(b)$ spectator $B$ from the
player? (c) How far are the spectators from each other?

Sandro Maludze

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Numerade Educator

Problem 2

What is the bulk modulus of oxygen if 32.0 g of oxygen occupies 22.4 $\mathrm{L}$ and the speed of sound in the oxygen is 317 $\mathrm{m} / \mathrm{s} ?$

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Problem 3

When the door of the Chapel of the Mausoleum in Hamilton, Scotland, is slammed shut, the last echo heard by someone standing just inside the door reportedly comes 15 s later. If
that echo were due to a single reflection off a wall opposite the
door, how far from the door is the wall? (b) If, instead, the wall is
25.7 $\mathrm{m}$ away, how many reflections (back and forth) occur?

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Problem 4

A column of soldiers, marching at 120 paces per minute, keep in step with the beat of a drummer at the head of the column. The
soldiers in the rear end of the column are striding forward with the
left foot when the drummer is advancing with the right foot. What is
the approximate length of the column?

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Problem 5

Earthquakes generate sound waves inside Earth. Unlike a gas, Earth can experience both transverse (S) and longitudinal (P) sound waves. Typically, the speed of S waves is about
$4.5 \mathrm{km} / \mathrm{s},$ and that of $\mathrm{P}$ waves 8.0 $\mathrm{km} / \mathrm{s} .$ A seismograph records $\mathrm{P}$ and $\mathrm{S}$ waves from an earthquake. The first $\mathrm{P}$ waves arrive 3.0 $\mathrm{min}$ before the first $S$ waves. If the waves travel in a straight line, how
far away did the earthquake occur?

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Problem 6

A man strikes one end of a thin rod with a hammer. The speed of sound in the rod is 15 times the speed of sound in air.
A woman, at the other end with her ear close to the rod, hears the
sound of the blow twice with a 0.12 s interval between; one sound comes through the rod and the other comes through the air along side the rod. If the speed of sound in air is $343 \mathrm{m} / \mathrm{s},$ what is the
length of the rod?

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Problem 7

A stone is dropped into a well. The splash is heard 3.00 s later. What is the depth of the well?

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Problem 8

Hot chocolate effect. Tap a metal spoon inside a mug of water and note the frequency $f_{i}$ you hear. Then add a
spoonful of powder (say, chocolate mix or instant coffee) and tap
again as you stir the powder. The frequency you hear has a lower value $f_{s}$ because the tiny air bubbles released by the powder
change the water's bulk modulus. As the bubbles reach the water
surface and disappear, the frequency gradually shifts back to its
initial value. During the effect, the bubbles don't appreciably
change the water's density or volume or the sound's wavelength.
Rather, they change the value of $d V / d p-$ that is, the differential
change in volume due to the differential change in the pressure
caused by the sound wave in the water. If $f_{s} / f_{i}=0.333,$ what is the
ratio $(d V / d p)_{s} /(d V / d p)_{i}^{?}$

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Numerade Educator

Problem 9

If the form of a sound wave traveling through air is
$$s(x, t)=(6.0 \mathrm{nm}) \cos (k x+(3000 \mathrm{rad} / \mathrm{s}) t+\phi)$$
how much time does any given air molecule along the path take to
move between displacements $s=+2.0 \mathrm{nm}$ and $s=-2.0 \mathrm{nm}$ ?

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Problem 10

Underwater illusion. One clue used by your brain to determine
the direction of a source of sound is
the time delay $\Delta t$ between the arrival
of the sound at the ear closer to the
source and the arrival at the farther ear. Assume that the source is distant
so that a wavefront from it is approximately planar when it reaches you,
and let $D$ represent the separation between your ears. (a) If the source is located at angle $\theta$ in front of
you (Fig. $17-31 )$, what is $\Delta t$ in terms of $D$ and the speed of sound $v$
in air? (b) If you are submerged in water and the sound source is directly to your right, what is $\Delta t$ in terms of $D$ and the speed of sound
$v_{w}$ in water? (c) Based on the time-delay clue, your brain interprets
the submerged sound to arrive at an angle $\theta$ from the forward direction. Evaluate $\theta$ for fresh water at $20^{\circ} \mathrm{C}$ .

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Problem 11

Diagnostic ultrasound of frequency 4.50 $\mathrm{MHz}$ is used to examine tumors in soft tisue. (a) What is the wavelength in air of
such a sound wave? (b) If the speed of sound in tissue is $1500 \mathrm{m} / \mathrm{s},$
what is the wavelength of this wave in tissue?

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Numerade Educator

Problem 12

The pressure in a traveling sound wave is given by the equation $$
\Delta p=(1.50 \mathrm{Pa}) \sin \pi\left[\left(0.900 \mathrm{m}^{-1}\right) x-\left(315 \mathrm{s}^{-1}\right) t\right]$$
Find the (a) pressure amplitude, (b) frequency, (c) wavelength, and
(d) speed of the wave.

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Problem 13

A sound wave of the form $s=s_{m} \cos (k x-\omega t+\phi)$ travels at 343 $\mathrm{m} / \mathrm{s}$ through air in a long horizontal tube. At one instant, air
molecule $A$ at $x=2.000 \mathrm{m}$ is at its maximum positive displace-
ment of 6.00 $\mathrm{nm}$ and air molecule $B$ at $x=2.070 \mathrm{m}$ is at a pos-
itive displacement of 2.00 $\mathrm{nm}$ .
All the molecules between $A$
and $B$ are at intermediate displacements. What is the frequency of the wave?

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Problem 14

Figure $17-32$ shows the output from a pressure monitor mounted at a point along the path taken by a sound wave of a single frequency traveling at 343 $\mathrm{m} / \mathrm{s}$ through air with a uniform density of $1.21 \mathrm{~kg} / \mathrm{m}^{3} .$ The vertical axis scale is set by $\Delta p_{s}=4.0 \mathrm{mPa}$. If the displacement function of the wave is $s(x, t)=s_{m} \cos (k x-\omega t),$ what are $(\mathrm{a}) s_{m},(\mathrm{~b}) k,$ and $(\mathrm{c}) \omega ?$ The air is then cooled so that its density is $1.35 \mathrm{~kg} / \mathrm{m}^{3}$ and the speed of a sound wave through it is $320 \mathrm{~m} / \mathrm{s}$. The sound source again emits the sound wave at the same frequency and same pressure amplitude. What now are (d) $s_{m},$ (e) $k,$ and (f) $\omega?$

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Problem 15

A handclap on stage in an amphitheater sends out sound waves that scatter from terraces of width $w=0.75 \mathrm{m}$
(Fig. $17-33 ) .$ The sound returns to the stage as a periodic
series of pulses, one from each terrace; the parade of pulses sounds like a played note. (a) Assuming that all the rays in
Fig. $17-33$ are horizontal, find the frequency at which the pulses
return (that is, the frequency of the perceived note). (b) If the
width $w$ of the terraces were smaller, would the frequency be
higher or lower?

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Numerade Educator

Problem 16

Two sound waves, from two different sources with the same frequency, 540 $\mathrm{Hz}$ , travel in the same direction at 330 $\mathrm{m} / \mathrm{s}$ . The
sources are in phase. What is the phase difference of the waves at
a point that is 4.40 $\mathrm{m}$ from one source and 4.00 $\mathrm{m}$ from the
other?

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Problem 17

Two loud speakers are located 3.35 $\mathrm{m}$ apart on an outdoor stage. A listener is 18.3 $\mathrm{m}$ from one and 19.5 $\mathrm{m}$ from the
other. During the sound check, a signal generator drives the two
speakers in phase with the same amplitude and frequency.
The transmitted frequency is swept through the audible range $(20 \mathrm{Hz}$ to 20 $\mathrm{kHz})$ . (a) What is the lowest frequency $f_{\mathrm{min}, 1}$ that gives minimum signal (destructive interference) at the listener's location? By what number must $f_{\min , 1}$ be multiplied to get (b) the second lowest frequency $f_{\text { min, } 2}$ that gives minimum signal and (c) the third lowest frequency $f_{\min , 3}$ that gives minimum signal? (d) What is the lowest frequency $f_{\text { max, } 1}$ that gives maximum signal (constructive interference) at the listener's location? By what number must $f_{\max , 1}$ be multiplied to get (e) the second lowest frequency $f_{\max , 2}$ that
gives maximum signal and (f) the third lowest frequency $f_{\max , 3}$ that
gives maximum signal?

Sandro Maludze

Numerade Educator

Problem 18

In Fig. $17-34,$ sound waves $A$ and $B,$ both of wavelength $\lambda,$ are initially in phase and traveling right-ward, as indicated by the two rays.
Wave $A$ is reflected from four surfaces but ends up traveling in its original direction. Wave $B$ ends in that direction after reflecting from two
surfaces. Let distance $L$ in the figure
be expressed as a multiple $q$ of $\lambda : L=$ q\lambda. What are the (a) smallest and (b) second smallest values of $q$ that
put $A$ and $B$ exactly out of phase with each other after the
reflections?

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Problem 19

Figure $17-35$ shows two isotropic point sources of sound, $S_{1}$
and $S_{2} .$ The sources emit waves in
phase at wavelength 0.50 $\mathrm{m}$ ; they are separated by $D=1.75 \mathrm{m} .$ If we move a sound detector along a large
circle centered at the midpoint between the sources, at how many
points do waves arrive at the detector (a) exactly in phase and (b) exactly out of phase?

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Problem 20

Figure $17-36$ shows four isotropic point sources of sound that are uniformly spaced on an $x$ axis. The sources emit sound at
the same wavelength $\lambda$ and same amplitude $s_{m}$ and they emit in
phase. A point $P$ is shown on the $x$ axis. Assume that as the sound waves travel to $P,$ the decrease in their amplitude is negligible.
What multiple of $s_{m}$ is the amplitude of the net wave at $P$ if distance $d$ in the figure is (a) $\lambda / 4,($ b) $\lambda / 2,$ and $(c) \lambda ?$

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Problem 21

In Fig. $17-37,$ two speakers separated by distance $d_{1}=2.00 \mathrm{m}$ are
in phase. Assume the amplitudes of
the sound waves from the speakers
are approximately the same at the listener's ear at distance $d_{2}=3.75 \mathrm{m}$ directly in front of one speaker.
Consider the full audible range for
normal hearing, 20 $\mathrm{Hz}$ to 20 $\mathrm{kHz}$ . (a)
What is the lowest frequency $f_{\min , 1}^{2}$ that gives minimum signal (destructive interference) at the listener's ear? By what number must $f_{\text { min, }}$ be multiplied to get (b)
the second lowest frequency $f_{\text { min, } 2}$ that gives minimum signal and (c) the third lowest frequency $f_{\text { min } 3,3}$ that gives minimum signal? (d) What is the lowest frequency $f_{\text { max, }}$ that gives maximum signal
(constructive interference) at the listener's ear? By what number must $f_{\max , 1}$ be multiplied to get (e) the second lowest frequency $f_{\max , 2}$ that gives maximum signal and (f) the third lowest frequency $f_{\text { maxs }}$ that gives maximum signal?

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Problem 22

In Fig. $17-38,$ sound with a 40.0 $\mathrm{cm}$ wavelength travels right-ward from a source and through a
tube that consists of a straight portion and a half-circle. Part of the
sound wave travels through the half-circle and then rejoins the rest of the
wave, which goes directly through
the straight portion. This rejoining
results in interference. What is the
smallest radius $r$ that results in an intensity minimum at the detector?

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Numerade Educator

Problem 23

Figure $17-39$ shows two point sources $S_{1}$ and $S_{2}$ that emit
sound of wavelength $\lambda=2.00 \mathrm{m} .$
The emissions are isotropic and in
phase, and the separation between the sources is $d=16.0 \mathrm{m} .$ At any point $P$ on the $x$ axis, the wave
from $S_{1}$ and the wave from $S_{2}$ interfere. When $P$ is very far away
$(x \approx \infty),$ what are (a) the phase difference between the arriving
waves from $S_{1}$ and $S_{2}$ and $(\mathrm{b})$ the type of interference they produce? Now move point $P$ along the $x$ axis toward $S_{1}$ (c) Does the
phase difference between the waves increase or decrease? At
what distance $x$ do the waves have a phase difference of (d)
$0.50 \lambda,(\mathrm{e}) 1.00 \lambda,$ and $(\mathrm{f}) 1.50 \lambda ?$

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Problem 24

Suppose that the sound level of a conversation is initially at an angry 70 $\mathrm{dB}$ and then drops to a soothing 50 $\mathrm{dB}$ . Assuming that
the frequency of the sound is 500 $\mathrm{Hz}$ , determine the (a) initial and
(b) final sound intensities and the (c) initial and (d) final sound
wave amplitudes.

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Problem 25

A sound wave of frequency 300 $\mathrm{Hz}$ has an intensity of 1.00$\mu \mathrm{W} / \mathrm{m}^{2} .$ What is the amplitude of the air oscillations caused by
this wave?

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Problem 26

A 1.0 $\mathrm{W}$ point source emits sound waves isotropically. Assuming that the energy of the waves is conserved, find the intensity (a) 1.0 $\mathrm{m}$ from the source and (b) 2.5 $\mathrm{m}$ from the source.

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Problem 27

A certain sound source is increased in sound level by 30.0 $\mathrm{dB}$ . By what multiple is (a) its intensity increased and (b) its pressure amplitude increased?

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Problem 28

Two sounds differ in sound level by 1.00 dB. What is the ratio of the greater intensity to the smaller intensity?

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Problem 29

A point source emits sound waves isotropically. The intensity of the waves 2.50 $\mathrm{m}$ from the source is $1.91 \times 10^{-4} \mathrm{W} / \mathrm{m}^{2}$ .
Assuming that the energy of the waves is conserved, find the
power of the source.

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Numerade Educator

Problem 30

The source of a sound wave has a power of 1.00$\mu \mathrm{W} .$ If it is a point source, (a) what is the intensity 3.00 $\mathrm{m}$ away and (b) what is
the sound level in decibels at that distance?

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Jayashree Behera

Numerade Educator

Problem 31

When you "crack" a knuckle, you suddenly widen the knuckle cavity, allowing more volume for the synovial fluid inside it and causing a gas bubble suddenly to appear in the fluid. The
sudden production of the bubble, called "cavitation," produces a
sound pulse $-$ the cracking sound. Assume that the sound is transmitted uniformly in all directions and that it fully passes from the
knuckle interior to the outside. If the pulse has a sound level of
62 dB at your ear, estimate the rate at which energy is produced by
the cavitation.

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Problem 32

Approximately a third of people with normal hearing have ears that continuously emit a low-intensity sound outward
through the ear canal. A person with such spontaneous otoacoustic
emission is rarely aware of the sound, except perhaps in a noise-free environment, but occasionally the emission is loud enough to be heard by someone else nearby. In one observation, the sound wave had a frequency of 1665 $\mathrm{Hz}$ and a pressure amplitude of $1.13 \times 10^{-3} \mathrm{Pa}$ . What were (a) the displacement amplitude and (b) the intensity of the wave emitted by the ear?

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Problem 33

Male Rana catesbeiana bullfrogs are known for their loud mating call. The call is emitted not by the frog's mouth but by
its eardrums, which lie on the surface of the head. And, surprisingly, the sound has nothing to do with the frog's inflated throat. If the emitted sound has a frequency of 260 $\mathrm{Hz}$ and a sound level of 85 $\mathrm{dB}($ near the eardrum), what is the amplitude of the eardrum's oscillation? The air density is 1.21 $\mathrm{kg} / \mathrm{m}^{3} .$

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Problem 34

Two atmospheric sound sources $A$ and $B$ emit isotropically at constant power. The sound levels $\beta$ of their emissions are
plotted in Fig. $17-40$ versus the radial distance $r$ from the sources.
The vertical axis scale is set by $\beta_{1}=85.0 \mathrm{dB}$ and $\beta_{2}=65.0 \mathrm{dB}$ .
What are (a) the ratio of the larger power to the smaller power and
(b) the sound level difference at $r=10 \mathrm{m} ?$

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Numerade Educator

Problem 35

A point source emits 30.0 $\mathrm{W}$ of sound isotropically. A small microphone intercepts the sound in an area of $0.750 \mathrm{cm}^{2}, 200 \mathrm{m}$
from the source. Calculate (a) the sound intensity there and (b) the
power intercepted by the microphone.

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Problem 36

Party hearing. As the number of people at a party increases, you must raise your voice for a listener to hear you against
the background noise of the other partygoers. However, once you
reach the level of yelling, the only way you can be heard is if you move closer to your listener, into the listener's "personal space."
Model the situation by replacing you with an isotropic point source
of fixed power $P$ and replacing your listener with a point that absorbs part of your sound waves. These points are initially separated
by $r_{i}=1.20 \mathrm{m} .$ If the background noise increases by $\Delta \beta=5 \mathrm{dB}$ , the
sound level at your listener must also increase. What separation $r_{f}$
is then required?

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Jayashree Behera

Numerade Educator

Problem 37

A sound source sends a sinusoidal sound wave of angular frequency 3000 rad/s and amplitude 12.0 $\mathrm{nm}$ through a tube of air.
The internal radius of the tube is 2.00 $\mathrm{cm} .$ (a) What is the average
rate at which energy (the sum of the kinetic and potential energies) is transported to the opposite end of the tube? (b) If, simultane-
ously, an identical wave travels along an adjacent, identical tube,
what is the total average rate at which energy is transported to the opposite ends of the two tubes by the waves? If, instead, those two
waves are sent along the same tube simultaneously, what is the total average rate at which they transport energy when their phase
difference is $(\mathrm{c}) 0,(\mathrm{d}) 0.40 \pi \mathrm{rad},$ and $(\mathrm{e}) \pi \mathrm{rad} ?$

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Problem 38

The water level in a vertical glass tube 1.00 $\mathrm{m}$ long can be adjusted to any position in the tube. A tuning fork vibrating at 686 $\mathrm{Hz}$
is held just over the open top end of the tube, to set up a standing
wave of sound in the air-filled top portion of the tube. (That air-filled top portion acts as a tube with one end closed and the other
end open.) (a) For how many different positions of the water level
will sound from the fork set up resonance in the tube's air-filled portion? What are the (b) least and (c) second least water heights
in the tube for resonance to occur?

Jayashree Behera

Jayashree Behera

Numerade Educator

Problem 39

(a) Find the speed of waves on a violin string of mass 800 $\mathrm{mg}$ and length 22.0 $\mathrm{cm}$ if the fundamental frequency is
920 $\mathrm{Hz} .$ (b) What is the tension in the string? For the fundamental,
what is the wavelength of (c) the waves on the string and (d) the
sound waves emitted by the string?

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Numerade Educator

Problem 40

Organ pipe $A,$ with both ends open, has a fundamental frequency of 300 $\mathrm{Hz}$ . The third harmonic of organ pipe $B,$ with
one end open, has the same frequency as the second harmonic of
pipe $A .$ How long are (a) pipe $A$ and (b) pipe $B$ ?

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Numerade Educator

Problem 41

A violin string 15.0 $\mathrm{cm}$ long and fixed at both ends oscillates in its $n=1$ mode. The speed of waves on the string is $250 \mathrm{m} / \mathrm{s},$ and
the speed of sound in air is 348 $\mathrm{m} / \mathrm{s} .$ What are the (a) frequency and
(b) wavelength of the emitted sound wave?

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Numerade Educator

Problem 42

A sound wave in a fluid medium is reflected at a barrier so that a standing wave is formed. The distance between nodes is
$3.8 \mathrm{cm},$ and the speed of propagation is 1500 $\mathrm{m} / \mathrm{s} .$ Find the frequency of the sound wave.

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Problem 43

In Fig. $17-41, S$ is a small loudspeaker driven by an audio oscillator with a frequency that
is varied from 11000 $\mathrm{Hz}$ two $2000 \mathrm{Hz},$ and $D$ is a cylindrical pipe with two open ends and a length of 45.7 $\mathrm{cm} .$ The speed of sound in the air-filled pipe is
344 $\mathrm{m} / \mathrm{s}$ . (a) At how many frequencies does the
sound from the loudspeaker set up resonance in
the pipe? What are the (b) lowest and (c) second
lowest frequencies at which resonance occurs?

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Numerade Educator

Problem 44

The crest of a Parasaurolophus dinosaur skull is shaped somewhat like a trombone and contains a nasal passage in the
form of a long, bent tube open at both ends. The dinosaur may
have used the passage to produce sound by setting up the fundamental mode in it. (a) If the nasal passage in a certain
Parasaurolophus fossil is 2.0 $\mathrm{m}$ long, what frequency would have
been produced? (b) If that dinosaur could be recreated (as in Jurassic Park , would a person with a hearing range of 60 $\mathrm{Hz}$ to
20 $\mathrm{kHz}$ be able to hear that fundamental mode and, if so, would the
sound be high or low frequency? Fossil skulls that contain shorter nasal passages are thought to be those of the female
Parasaurolophus. (c) Would that make the female's fundamental
frequency higher or lower than the male's?

Jayashree Behera

Jayashree Behera

Numerade Educator

Problem 45

In pipe $A,$ the ratio of a particular harmonic frequency to the next lower harmonic frequency is $1.2 .$ In pipe $B,$ the ratio of a particular harmonic frequency to the next lower harmonic frequency is $1.4 .$ How many open ends are in (a) pipe $A$ and (b) pipe $B$ ?

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Numerade Educator

Problem 46

Pipe $A,$ which is 1.20 $\mathrm{m}$ long and open at both ends, oscillates at its third lowest harmonic frequency. It is filled with air
for which the speed of sound is 343 $\mathrm{m} / \mathrm{s} .$ Pipe $B,$ which is closed at
one end, oscillates at its second lowest harmonic frequency. This frequency of $B$ happens to match the frequency of $A .$ An $x$ axis extends along the interior of $B$ , with $x=0$ at the closed end. (a) How
many nodes are along that axis? What are the (b) smallest and
(c) second smallest value of $x$ locating those nodes? (d) What is the
fundamental frequency of $B$ ?

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Problem 47

A well with vertical sides and water at the bottom resonates at 7.00 $\mathrm{Hz}$ and at no lower frequency. The air-filled portion of the
well acts as a tube with one closed end (at the bottom) and one
open end (at the top). The air in the well has a density of 1.10 $\mathrm{kg} / \mathrm{m}^{3}$
and a bulk modulus of $1.33 \times 10^{5}$ Pa. How far down in the well is
the water surface?

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Numerade Educator

Problem 48

One of the harmonic frequencies of tube $A$ with two open ends is 325 Hz. The next-highest harmonic frequency is 390 $\mathrm{Hz}$ .
(a) What harmonic frequency is next highest after the harmonic
frequency 195 $\mathrm{Hz}$ ? (b) What is the number of this next-highest
harmonic? One of the harmonic frequencies of tube $B$ with only one open end is 1080 $\mathrm{Hz}$ . The next-highest harmonic frequency is
1320 $\mathrm{Hz}$ . (c) What harmonic frequency is next highest after the
harmonic frequency 600 $\mathrm{Hz}$ ? (d) What is the number of this next-
highest harmonic?

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Numerade Educator

Problem 49

A violin string 30.0 $\mathrm{cm}$ long with linear density 0.650 $\mathrm{g} / \mathrm{m}$ is placed near a loudspeaker that is fed by an audio oscillator of variable frequency. It is found that the string is set into oscillation only at the frequencies 880 and 1320 $\mathrm{Hz}$ as the frequency of the oscillator is varied over the range $500-150 \mathrm{Hz}$ . What is the tension in the string?

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Numerade Educator

Problem 50

A tube 1.20 $\mathrm{m}$ long is closed at one end. A stretched wire is placed near the open end. The wire is 0.330 $\mathrm{m}$ long and has a
mass of 9.60 $\mathrm{g} .$ It is fixed at both ends and oscillates in its fundamental mode. By resonance, it sets the air column in the tube into
oscillation at that column's fundamental frequency. Find (a) that
frequency and (b) the tension in the wire.

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Jayashree Behera

Numerade Educator

Problem 51

The A string of a violin is a little too tightly stretched. Beats at 4.00 per second are heard when the string is sounded together
with a tuning fork that is oscillating accurately at concert $\mathrm{A}$
$(440 \mathrm{Hz}) .$ What is the period of the violin string oscillation?

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Numerade Educator

Problem 52

A tuning fork of unknown frequency makes 3.00 beats per second with a standard fork of frequency 384 Hz. The beat frequency decreases when a small piece of wax is put on a prong of the first fork. What is the frequency of this fork?

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Problem 53

Two identical piano wires have a fundamental frequency of 600 $\mathrm{Hz}$ when kept under the same tension. What fractional increase in the tension of one wire will lead to the occurrence of 6.0 beats/s when both wires oscillate simultaneously?

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Numerade Educator

Problem 54

You have five tuning forks that oscillate at close but different resonant frequencies. What are the (a) maximum and (b) minimum number of different beat frequencies you can produce by sounding the forks two at a time, depending on how the resonant
frequencies differ?

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Numerade Educator

Problem 55

A whistle of frequency 540 Hz moves in a circle of radius 60.0 $\mathrm{cm}$ at an angular speed of 15.0 $\mathrm{rad} / \mathrm{s}$ . What are the (a) lowest
and (b) highest frequencies heard by a listener a long distance
away, at rest with respect to the center of the circle?

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Numerade Educator

Problem 56

An ambulance with a siren emitting a whine at 1600 Hz over takes and passes a cyclist pedaling a bike at 2.44 $\mathrm{m} / \mathrm{s}$ . After being
passed, the cyclist hears a frequency of 1590 $\mathrm{Hz} .$ How fast is the
ambulance moving?

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Numerade Educator

Problem 57

A state trooper chases a speeder along a straight road; both vehicles move at 160 $\mathrm{km} / \mathrm{h}$ . The siren on the trooper's vehicle produces sound at a frequency of 500 $\mathrm{Hz}$ . What is the Doppler shift in
the frequency heard by the speeder?

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Numerade Educator

Problem 58

A sound source $A$ and a reflecting surface $B$ move directly toward each other. Relative to the air, the speed of source $A$ is
29.9 $\mathrm{m} / \mathrm{s}$ , the speed of surface $B$ is 65.8 $\mathrm{m} / \mathrm{s}$ , and the speed of sound
is 329 $\mathrm{m} / \mathrm{s}$ . The source emits waves at frequency 1200 $\mathrm{Hz}$ as measured in the source frame. In the reflector frame, what are the
(a) frequency and (b) wavelength of the arriving sound waves? In
the source frame, what are the (c) frequency and (d) wavelength of
the sound waves reflected back to the source?

Jayashree Behera

Jayashree Behera

Numerade Educator

Problem 59

In Fig. $17-42,$ a French submarine and a U.S. submarine move toward each other during maneuvers in motionless water
in the North Atlantic. The French sub moves at speed $v_{F}=$
$50.00 \mathrm{km} / \mathrm{h},$ and the U.S. sub at $v_{\mathrm{US}}=70.00 \mathrm{km} / \mathrm{h}$ . The French sub sends out a sonar signal (sound wave in water) at $1.000 \times 10^{3} \mathrm{Hz}$ .
Sonar waves travel at 5470 $\mathrm{km} / \mathrm{h}$ . (a) What is the signal's frequency
as detected by the U.S. sub? (b) What frequency is detected by the
French sub in the signal reflected back to it by the U.S. sub?

Sandro Maludze

Numerade Educator

Problem 60

A stationary motion detector sends sound waves of frequency 0.150 $\mathrm{MHz}$ toward a truck approaching at a speed of 45.0 $\mathrm{m} / \mathrm{s}$ . What
is the frequency of the waves reflected back to the detector?

Jayashree Behera

Jayashree Behera

Numerade Educator

Problem 61

A bat is flitting about in a cave, navigating via ultrasonic bleeps. Assume that the sound emission frequency of the
bat is 39000 $\mathrm{Hz}$ . During one fast swoop directly toward a flat wall
surface, the bat is moving at 0.025 times the speed of sound in air.
What frequency does the bat hear reflected off the wall?

Sandro Maludze

Numerade Educator

Problem 62

Figure $17-43$ shows four tubes with lengths 1.0 $\mathrm{m}$ or $2.0 \mathrm{m},$ with one or two open ends as drawn. The third harmonic is set up in
each tube, and some of the sound that escapes from them is detected
by detector $D,$ which moves directly away from the tubes. In terms of the speed of sound $v$
what speed must the detector
have such that the detected
frequency of the sound from
(a) tube $1,$ (b) tube $2,$ (c) tube
$3,$ and (d) tube 4 is equal to the
tube's fundamental frequency?

Jayashree Behera

Jayashree Behera

Numerade Educator

Problem 63

An acoustic burglar alarm consists of a source emitting waves of frequency 28.0 $\mathrm{kHz}$ . What is the beat frequency between
the source waves and the waves reflected from an intruder walking
at an average speed of 0.950 $\mathrm{m} / \mathrm{s}$ directly away from the alarm?

Sandro Maludze

Numerade Educator

Problem 64

A stationary detector measures the frequency of a sound source that first moves at constant velocity directly toward the detector and then (after passing the detector) directly away from it. The emitted frequency is $f$ . During the approach the detected frequency is $f_{\text { app }}^{\prime}$ and during the recession it is $f_{\mathrm{rec}}^{\prime}$ If $\left(f_{\mathrm{app}}^{\prime}-f_{\mathrm{rec}}^{\prime}\right) / f=$
$0.500,$ what is the ratio $v_{s} / v$ of the speed of the source to the speed
of sound?

Jayashree Behera

Jayashree Behera

Numerade Educator

Problem 65

A 2000 Hz siren and a civil defense official are both at rest with respect to the ground. What frequency does the official hear if the wind is blowing at 12 $\mathrm{m} / \mathrm{s}$ (a) from source to official and (b) from official to source?

Sandro Maludze

Numerade Educator

Problem 66

Two trains are traveling toward each other at 30.5 $\mathrm{m} / \mathrm{s}$ relative to the ground. One train is blowing a whistle at 500 $\mathrm{Hz}$ .
(a) What frequency is heard on the other train in still air? (b) What
frequency is heard on the other train if the wind is blowing at 30.5 $\mathrm{m} / \mathrm{s}$ toward the whistle and away from the listener? (c) What
frequency is heard if the wind direction is reversed?

Jayashree Behera

Jayashree Behera

Numerade Educator

Problem 67

A girl is sitting near the open window of a train that is moving at a velocity of 10.00 $\mathrm{m} / \mathrm{s}$ to the east. The girl's
uncle stands near the tracks and watches the train move away. The locomotive whistle emits sound at frequency 500.0 $\mathrm{Hz}$ . The air is
still. (a) What frequency does the uncle hear? (b) What frequency
does the girl hear? A wind begins to blow from the east at 10.00
$\mathrm{m} / \mathrm{s} .$ (c) What frequency does the uncle now hear? (d) What frequency does the girl now hear?

Sandro Maludze

Numerade Educator

Problem 68

The shock wave off the cockpit of the FA 18 in Fig. $17-24$ has an angle of about $60^{\circ} .$ The airplane was traveling at about
1350 $\mathrm{km} / \mathrm{h}$ when the photograph was taken. Approximately what
was the speed of sound at the airplane's altitude?

Jayashree Behera

Jayashree Behera

Numerade Educator

Problem 69

A jet plane passes over you at a height of 5000 $\mathrm{m}$ and a speed of Mach 1.5 (a) Find the Mach cone angle (the sound speed is 331 $\mathrm{m} / \mathrm{s} )$ . (b) How long after the jet passes directly overhead does the shock wave reach you?

Sandro Maludze

Numerade Educator

Problem 70

A plane flies at 1.25 times the speed of sound. Its sonic boom reaches a man on the ground 1.00 min after the plane passes directly overhead. What is the altitude of the plane? Assume the speed of sound to be 330 $\mathrm{m} / \mathrm{s}$.

Jayashree Behera

Jayashree Behera

Numerade Educator

Problem 71

At a distance of $10 \mathrm{km},$ a 100 $\mathrm{Hz}$ horn, assumed to be an isotropic point source, is barely audible. At what distance would it
begin to cause pain?

Sandro Maludze

Numerade Educator

Problem 72

A bullet is fired with a speed of 685 $\mathrm{m} / \mathrm{s} .$ Find the angle made by the shock cone with the line of motion of the bullet.

Jayashree Behera

Jayashree Behera

Numerade Educator

Problem 73

A sperm whale (Fig. $17-44 a$ ) vocalizes by producing a series of clicks. Actually, the whale makes only a single sound near
the front of its head to start the series. Part of that sound then
emerges from the head into the water to become the first click of the series. The rest of the sound travels backward through the
spermaceti sac (a body of fat), reflects from the frontal sac (an air
layer), and then travels forward through the spermaceti sac. When
it reaches the distal sac (another air layer) at the front of the head, some of the sound escapes into the water to form the second click,
and the rest is sent back through the spermaceti sac (and ends up
forming later clicks). Figure $17-44 b$ shows a strip-chart recording of a series of clicks.
A unit time interval of 1.0 $\mathrm{ms}$ is indicated on the chart. Assuming
that the speed of sound in the spermaceti sac is $1372 \mathrm{m} / \mathrm{s},$ find
the length of the spermaceti sac. From such a calculation, marine
scientists estimate the length of a whale from its click series.

Sandro Maludze

Numerade Educator

Problem 74

The average density of Earth's crust 10 $\mathrm{km}$ beneath the continents is 2.7 $\mathrm{g} / \mathrm{cm}^{3} .$ The speed of longitudinal seismic waves at that
depth, found by timing their arrival from distant earthquakes, is
5.4 $\mathrm{km} / \mathrm{s}$ . Find the bulk modulus of Earth's crust at that depth. For
comparison, the bulk modulus of steel is about $16 \times 10^{10} \mathrm{Pa.}$

Jayashree Behera

Jayashree Behera

Numerade Educator

Problem 75

A certain loudspeaker system emits sound isotropically with a frequency of 2000 $\mathrm{Hz}$ and an intensity of 0.960 $\mathrm{mW} / \mathrm{m}^{2}$ at a
distance of 6.10 $\mathrm{m} .$ Assume that there are no reflections. (a) What
is the intensity at 30.0 $\mathrm{m} ?$ At $6.10 \mathrm{m},$ what are (b) the displacement amplitude and (c) the pressure amplitude?

Sandro Maludze

Numerade Educator

Problem 76

Find the ratios (greater to smaller) of the (a) intensities, (b) pressure amplitudes, and (c) particle displacement amplitudes
for two sounds whose sound levels differ by 37 dB.

Jayashree Behera

Jayashree Behera

Numerade Educator

Problem 77

In Fig. $17-45,$ sound waves $A$ and $B,$ both of wavelength $\lambda,$ are initially in phase and traveling rightward, as indicated by the two rays.
Wave $A$ is reflected from four surfaces but ends up traveling in its original direction. What multiple of
wavelength $\lambda$ is the smallest value of
distance $L$ in the figure that puts $A$
and $B$ exactly out of phase with each $A$
other after the reflections?

Sandro Maludze

Numerade Educator

Problem 78

A trumpet player on a moving railroad flatcar moves toward a second trumpet player standing alongside the track while both play
a 440 Hz note. The sound waves heard by a stationary observer between the two players have a beat frequency of 4.0 beats/s. What is the flatcar's speed?

Jayashree Behera

Jayashree Behera

Numerade Educator

Problem 79

In Fig. $17-46$ , sound of wavelength 0.850 $\mathrm{m}$ is emitted isotropically by point source $S .$ Sound ray 1 extends directly to
detector $D,$ at distance $L=10.0 \mathrm{m}$ . Sound ray 2 extends to $D$ via a
reflection (effectively, a "bouncing") of the sound at a flat surface. That reflection occurs on a perpendicular bisector to the $S D$ line,
at distance $d$ from the line. Assume that the reflection shifts the
sound wave by 0.500$\lambda$ . For what least value of $d$ (other than zero)
do the direct sound and the reflected sound arrive at $D($ a) exactly
out of phase and (b) exactly in phase?

Sandro Maludze

Numerade Educator

Problem 80

A detector initially moves at constant velocity directly toward a stationary sound source and then (after passing it) directly from it. The emitted frequency is $f$ . During the approach the detected frequency is $f_{\text { app }}^{\prime}$ and during the recession it is $f_{\text { rec. }}^{\prime}$ . If the
frequencies are related by $\left(f_{\text { app }}^{\prime}-f_{\text { rec }}^{\prime}\right) / f=0.500,$ what is the ratio
$v_{D} / v$ of the speed of the detector to the speed of sound?

Jayashree Behera

Jayashree Behera

Numerade Educator

Problem 81

(a) If two sound waves, one in air and one in (fresh) water, are equal in intensity and angular frequency, what is the
ratio of the pressure amplitude of the wave in water to that of
the wave in air? Assume the water and the air are at $20^{\circ} \mathrm{C}$ . See
Table $14-1 .$ ) If the pressure amplitudes are equal instead, what
is the ratio of the intensities of the waves?

Sandro Maludze

Numerade Educator

Problem 82

A continuous sinusoidal longitudinal wave is sent along a very long coiled spring from an attached oscillating source. The wave
travels in the negative direction of an $x$ axis; the source frequency
is $25 \mathrm{Hz} ;$ at any instant the distance between successive points of
maximum expansion in the spring is 24 $\mathrm{cm}$ ; the maximum longitudinal displacement of a spring particle is $0.30 \mathrm{cm} ;$ and the particle
at $x=0$ has zero displacement at time $t=0 .$ If the wave is written in the form $s(x, t)=s_{m} \cos (k x \pm \omega t),$ what are (a) $s_{m},$ (b) $k,(\mathrm{c}) \omega$ (d) the wave speed, and (e) the correct choice of sign in front of $\omega ?$

Jayashree Behera

Jayashree Behera

Numerade Educator

Problem 83

Ultrasound, which consists of sound waves with frequencies
above the human audible range, can
be used to produce an image of the
interior of a human body. Moreover,
ultrasound can be used to measure
the speed of the blood in the body; it does so by comparing the frequency of the ultrasound sent into the
body with the frequency of the ultrasound reflected back to the
body's surface by the blood. As the blood pulses, this detected frequency varies. Suppose that an ultrasound image of the arm of a patient shows an artery that is angled at $\theta=20^{\circ}$ to the ultrasound's line of travel
(Fig. $17-47 ) .$ Suppose also that the frequency of the ultrasound
reflected by the blood in the artery is increased by a maximum of 5495 Hz from the original ultrasound frequency of $5.000,000 \mathrm{MHz}$ .
(a) In Fig. $17-47$ , is the direction of the blood flow rightward or
leftward? (b) The speed of sound in the human arm is 1540 $\mathrm{m} / \mathrm{s}$ . What is the maximum speed of the blood? (Hint: The Doppler effect
is caused by the component of the blood's velocity along the ultrasound's direction of travel.) (c) If angle $\theta$ were greater, would the reflected frequency be greater or less?

Sandro Maludze

Numerade Educator

Problem 84

The speed of sound in a certain metal is $v_{m}$ . One end of a long pipe of that metal of length $L$ is struck a hard blow.
A listener at the other end hears two sounds, one from the wave
that travels along the pipe's metal wall and the other from the wave that travels through the air inside the pipe. (a) If $v$ is the
speed of sound in air, what is the time interval $\Delta t$ between the arrivals of the two sounds at the listener's ear? (b) If $\Delta t=1.00$ s and
the metal is steel, what is the length $L ?$

Jayashree Behera

Jayashree Behera

Numerade Educator

Problem 85

An avalanche of sand along some rare desert sand dunes can produce a booming that is loud enough to be heard 10 $\mathrm{km}$
away. The booming apparently results from a periodic oscillation
of the sliding layer of sand- the layer's thickness expands and
contracts. If the emitted frequency is 90 $\mathrm{Hz}$ , what are (a) the period
of the thickness oscillation and (b) the wavelength of the sound?

Sandro Maludze

Numerade Educator

Problem 86

A sound source moves along an $x$ axis, between detectors $A$ and $B .$ The wavelength of the sound detected at $A$ is 0.500 that of
the sound detected at $B$ . What is the ratio $v_{s} / v$ of the speed of the
source to the speed of sound?

Jayashree Behera

Jayashree Behera

Numerade Educator

Problem 87

A siren emitting a sound of frequency 1000 Hz moves away from you toward the face of a cliff at a speed of 10 $\mathrm{m} / \mathrm{s}$ . Take
the speed of sound in air as 330 $\mathrm{m} / \mathrm{s}$ . (a) What is the frequency of
the sound you hear coming directly from the siren? (b) What is the frequency of the sound you hear reflected off the cliff? (c) What is
the beat frequency between the two sounds? Is it perceptible (less
than 20 $\mathrm{Hz}$ ?

Sandro Maludze

Numerade Educator

Problem 88

At a certain point, two waves produce pressure variations given by $\Delta p_{1}=\Delta p_{m} \sin \omega t$ and $\Delta p_{2}=\Delta p_{m} \sin (\omega t-\phi) .$ At this point, what is the ratio $\Delta p_{r} / \Delta p_{m},$ where $\Delta p_{r}$ is the pressure amplitude of the resultant wave, if $\phi$ is (a) $0,($ b) $) \pi / 2,($ c) $\pi / 3,$ and $(\mathrm{d}) \pi / 4 ?$

Jayashree Behera

Jayashree Behera

Numerade Educator

Problem 89

Two sound waves with an amplitude of 12 $\mathrm{nm}$ and a wavelength of 35 $\mathrm{cm}$ travel in the same direction through a long tube,
with a phase difference of $\pi / 3$ rad. What are the (a) amplitude and
(b) wavelength of the net sound wave produced by their interference? If, instead, the sound waves through the tube in opposite directions, what are the (c) amplitude and (d) wavelength of the net wave?

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 90

A sinusoidal sound wave moves at 343 $\mathrm{m} / \mathrm{s}$ through air in the positive direction of an $x$ axis. At one instant during the oscillations, air molecule $A$ is at its maximum displacement in the negative direction of the axis while air molecule $B$ is at its equilibrium position. The separation between those molecules is $15.0 \mathrm{cm},$ and the molecules between $A$ and $B$ have intermediate displacements
in the negative direction of the axis. (a) What is the frequency of the sound wave?
In a similar arrangement but for a different sinusoidal sound
wave, at one instant air molecule $C$ is at its maximum displacement
in the positive direction while molecule $D$ is at its maximum displacement in the negative direction. The separation between the
molecules is again $15.0 \mathrm{cm},$ and the molecules between $C$ and $D$
have intermediate displacements. (b) What is the frequency of the
sound wave?

Jayashree Behera

Jayashree Behera

Numerade Educator

Problem 91

Two identical tuning forks can oscillate at 440 Hz. A person is located somewhere on the line between them. Calculate the beat
frequency as measured by this individual if (a) she is standing still
and the tuning forks move in the same direction along the line at $3.00 \mathrm{m} / \mathrm{s},$ and $(\mathrm{b})$ the tuning forks are stationary and the listener
moves along the line at $3,00 \mathrm{m} / \mathrm{s}$ .

Sandro Maludze

Numerade Educator

Problem 92

You can estimate your distance from a lightning stroke by counting the seconds between the flash you see and the thunder
you later hear. By what integer should you divide the number of
seconds to get the distance in kilometers?

Jayashree Behera

Jayashree Behera

Numerade Educator

Problem 93

Figure $17-48$ shows an air-filled, acoustic interferometer, used
to demonstrate the interference of
sound waves. Sound source $S$ is an
oscillating diaphragm; $D$ is a sound detector, such as the ear or a microphone. Path $S B D$ can be varied in length, but path $S A D$ is fixed. At $D$
the sound wave coming along path $S B D$ interferes with that coming along path $S A D .$ In one demonstration, the sound intensity at $D$ has a minimum value of
100 units at one position of the movable arm and continuously climbs to a maximum value of 900 units when that arm is shifted
by 1.65 $\mathrm{cm} .$ Find (a) the frequency of the sound emitted by the
source and (b) the ratio of the amplitude at $D$ of the $S A D$ wave to that of the $S B D$ wave. (c) How can it happen that these waves
have different amplitudes, considering that they originate at the
same source?

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 94

On July $10,1996,$ a granite block broke away from a wall in Yosemite Valley and, as it began to slide down the wall, was
launched into projectile motion. Seismic waves produced by its
impact with the ground triggered seismographs as far away as 200 $\mathrm{km} .$ Later measurements indicated that the block had a mass
between $7.3 \times 10^{7} \mathrm{kg}$ and $1.7 \times 10^{8} \mathrm{kg}$ and that it landed 500 $\mathrm{m}$
vertically below the launch point and 30 $\mathrm{m}$ horizontally from it. (The launch angle is not known.) (a) Estimate the block's kinetic
energy just before it landed.
Consider two types of seismic waves that spread from the impact point $-a$ hemispherical body wave traveled through the
ground in an expanding hemisphere and a cylindrical surface wave traveled along the ground in an expanding shallow vertical cylin-
der (Fig. $17-49 )$ . Assume that the impact lasted 0.50 s, the vertical
cylinder had a depth $d$ of $5.0 \mathrm{m},$ and each wave type received 20$\%$
of the energy the block had just before impact. Neglecting any mechanical energy loss the waves experienced as they traveled,
determine the intensities of (b) the body wave and (c) the surface
wave when they reached a seismograph 200 $\mathrm{km}$ away. (d) On the
basis of these results, which wave is more easily detected on a
distant seismograph?

Jayashree Behera

Jayashree Behera

Numerade Educator

Problem 95

The sound intensity is 0.0080 $\mathrm{W} / \mathrm{m}^{2}$ at a distance of 10 $\mathrm{m}$ from an isotropic point source of sound. (a) What is the power of
the source? (b) What is the sound intensity 5.0 $\mathrm{m}$ from the source?
(c) What is the sound level 10 m from the source?

Sandro Maludze

Numerade Educator

Problem 96

Four sound waves are to be sent through the same tube of air, in the same direction:
$$\begin{aligned} s_{1}(x, t) &=(9.00 \mathrm{nm}) \cos (2 \pi x-700 \pi t) \\ s_{2}(x, t) &=(9.00 \mathrm{nm}) \cos (2 \pi x-700 \pi t+0.7 \pi) \\ s_{3}(x, t) &=(9.00 \mathrm{nm}) \cos (2 \pi x-700 \pi t+\pi) \\ s_{4}(x, t) &=(9.00 \mathrm{nm}) \cos (2 \pi x-700 \pi t+1.7 \pi) \end{aligned}$$
What is the amplitude of the resultant wave? (Hint: Use a phasor
diagram to simplify the problem.)

Jayashree Behera

Jayashree Behera

Numerade Educator

Problem 97

Straight line $A B$ connects two point sources that are 5.00 $\mathrm{m}$ apart, emit 300 $\mathrm{Hz}$ sound waves of the same amplitude, and emit
exactly out of phase. (a) What is the shortest distance between the
midpoint of $A B$ and a point on $A B$ where the interfering waves cause maximum oscillation of the air molecules? What are the (b) second and (c) third shortest distances?

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 98

A point source that is stationary on an $x$ axis emits a sinusoidal sound wave at a frequency of 686 $\mathrm{Hz}$ and speed 343 $\mathrm{m} / \mathrm{s}$ .
The wave travels radially outward from the source, causing air molecules to oscillate radially inward and outward. Let us define a wavefront as a line that connects points where the air molecules have the maximum, radially outward displacement. At any given
instant, the wavefronts are concentric circles that are centered on the source. (a) Along $x,$ what is the adjacent wavefront separation? Next, the source moves along $x$ at a speed of 110 $\mathrm{m} / \mathrm{s}$ . Along $x$ ,what are the wavefront separations (b) in front of and (c) behind
the source?

Jayashree Behera

Jayashree Behera

Numerade Educator

Problem 99

You are standing at a distance $D$ from an isotropic point source of sound. You walk 50.0 $\mathrm{m}$ toward the source and observe that the
intensity of the sound has doubled. Calculate the distance $D$ .

Sandro Maludze

Numerade Educator

Problem 100

Pipe $A$ has only one open end; pipe $B$ is four times as long and has two open ends. Of the lowest 10 harmonic numbers $n_{B}$ of
pipe $B,$ what are the (a) smallest, (b) second smallest, and (c) third
smallest values at which a harmonic frequency of $B$ matches one of
the harmonic frequencies of $A ?$

Jayashree Behera

Jayashree Behera

Numerade Educator

Problem 101

A pipe 0.60 $\mathrm{m}$ long and closed at one end is filled with an unknown gas. The third lowest harmonic frequency for the pipe is
750 $\mathrm{Hz}$ (a) What is the speed of sound in the unknown gas?
(b) What is the fundamental frequency for this pipe when it is filled
with the unknown gas?

Sandro Maludze

Numerade Educator

Problem 102

A sound wave travels out uniformly in all directions from a point source. (a) Justify the following expression for the displacement $s$ of the transmitting medium at any distance $r$ from the source:
$$s=\frac{b}{r} \sin k(r-v t)$$
where $b$ is a constant. Consider the speed, direction of propagation, periodicity, and intensity of the wave. (b) What is the dimension of the constant $b$ ?

Jayashree Behera

Jayashree Behera

Numerade Educator

Problem 103

A police car is chasing a speeding Porsche $911 .$ Assume that the Porsche's maximum speed is 80.0 $\mathrm{m} / \mathrm{s}$ and the police car's is 54.0
$\mathrm{m} / \mathrm{s}$ . At the moment both cars reach their maximum speed, what frequency will the Porsche driver hear if the frequency of the police
car's siren is 440 $\mathrm{Hz}$ ? Take the speed of sound in air to be 340 $\mathrm{m} / \mathrm{s}$ .

Sandro Maludze

Numerade Educator

Problem 104

Suppose a spherical loudspeaker emits sound isotropically at 10 $\mathrm{W}$ into a room with completely absorbent walls, floor, and ceiling
(an anechoic chamber).(a) What is the intensity of the sound at
distance $d=3.0 \mathrm{m}$ from the center of the source? (b) What is the
ratio of the wave amplitude at $d=4.0 \mathrm{m}$ to that at $d=3.0 \mathrm{m} ?$

Jayashree Behera

Jayashree Behera

Numerade Educator

Problem 105

In Fig. $17-35, S_{1}$ and $S_{2}$ are two isotropic point sources of sound. They emit waves in phase at wavelength 0.50 $\mathrm{m}$ ; they are
separated by $D=1.60 \mathrm{m} .$ If we move a sound detector along a
large circle centered at the midpoint between the sources, at how
many points do waves arrive at the detector (a) exactly in phase
and (b) exactly out of phase?

Sandro Maludze

Numerade Educator

Problem 106

Figure $17-50$ shows a transmitter and receiver of waves contained in a single instrument. It is used to measure the speed $u$ of a
target object (idealized as a flat plate) that is moving directly toward the unit, by analyzing the waves reflected from the target.
What is $u$ if the emitted frequency is 18.0 $\mathrm{kHz}$ and the detected frequency (of the returning waves) is 22.2 $\mathrm{kHz}$ ?

Jayashree Behera

Jayashree Behera

Numerade Educator

Problem 107

Kundt's method for measuring the speed of sound. In Fig. $17-51,$ a rod $R$ is clamped at its center; a disk $D$ at its end projects
into a glass tube that has cork filings spread over its interior. A plunger $P$ is provided at the other end of the tube, and the tube is
filled with a gas. The rod is made to oscillate longitudinally at frequency $f$ to produce sound waves inside the gas, and the location
of the plunger is adjusted until a standing sound wave pattern is set up inside the tube. Once the standing wave is set up, the motion of the gas molecules causes the cork filings to collect in a
pattern of ridges at the displacement nodes. If $f=4.46 \times 10^{3} \mathrm{Hz}$
and the separation between ridges is $9.20 \mathrm{cm},$ what is the speed of
sound in the gas?

Sandro Maludze

Numerade Educator

Problem 108

A source $\mathrm{S}$ and a detector $\mathrm{D}$ of radio waves are a distance $d$ apart on level ground (Fig. $17-52 ) .$ Radio waves of wavelength $\lambda$
reach $D$ either along a straight path or by reflecting (bouncing) $\lambda$
from a certain layer in the atmosphere. When the layer is at height
$H,$ the two waves reaching $D$ are exactly in phase. If the layer gradually rises, the phase difference between the two waves gradually
shifts, until they are exactly out of phase when the layer is at height
$H+h .$ Express $\lambda$ in terms of $d, h,$ and $H .$

Jayashree Behera

Jayashree Behera

Numerade Educator

Problem 109

In Fig. $17-53,$ a point source $S$ of sound waves lies near a reflecting wall $A B .$ A sound detector $D$ intercepts sound ray $R_{1}$
traveling directly from $S .$ It also intercepts sound ray $R_{2}$ that reflects from the wall such that the angle of incidence $\theta_{i}$ is equal to the angle of reflection $\theta_{r}$ Assume that the reflection of sound by
the wall causes a phase shift of 0.500$\lambda$ If the distances are $d_{1}=$
$2.50 \mathrm{m}, d_{2}=20.0 \mathrm{m},$ and $d_{3}=12.5 \mathrm{m},$ what are the (a) lowest and
(b) second lowest frequency at which $R_{1}$ and $R_{2}$ and $R_{2}$ are in phase at $D ?$

Manish Jain

Numerade Educator

Problem 110

A person on a railroad car blows a trumpet note at 440 $\mathrm{Hz}$ The car is moving toward a wall at 20.0 $\mathrm{m} / \mathrm{s}$ . Find the sound frequency (a) at the wall and (b) reflected back to the trumpeter.

Jayashree Behera

Jayashree Behera

Numerade Educator

Problem 111

A listener at rest (with respect to the air and the ground) hears a signal of frequency $f_{1}$ from a source moving toward him with a velocity of 15 $\mathrm{m} / \mathrm{s}$ , due east. If the listener then moves toward the approaching source with a velocity of 25 $\mathrm{m} / \mathrm{s}$ , due west, he hears a frequency $f_{2}$ that differs from $f_{1}$ by 37 Hz. What is the frequency of the source? (Take the speed of sound in air to be 340 $\mathrm{m} / \mathrm{s}$ .)

Sandro Maludze

Numerade Educator