College Physics

Raymond A. Serway, Jerry S. Faughn, Chris Vuille

Chapter 14

Sound - all with Video Answers

Educators

Chapter Questions

Problem 1

Suppose you hear a clap of thunder $16.2 \mathrm{~s}$ after seeing the associated lightning stroke. The speed of sound waves in air is $343 \mathrm{~m} / \mathrm{s}$, and the speed of light in air is $3.00 \times 10^{8} \mathrm{~m} / \mathrm{s}$. How far are you from the lightning stroke? Do you need to know the value of the speed of light to answer? Explain.

Prabhu Ramji

Prabhu Ramji

Numerade Educator

Problem 2

Earthquakes at fault lines in Earth's crust create seismic waves, which are longitudinal (P-waves) or transverse (Swaves). The P-waves have a speed of about $7 \mathrm{~km} / \mathrm{s}$. Estimate the average bulk modulus of Earth's crust given that the density of rock is about $2500 \mathrm{~kg} / \mathrm{m}^{3}$.

Prabhu Ramji

Numerade Educator

Problem 2

A sound wave from a siren has an inteasity of $100.0 \mathrm{~W} / \mathrm{m}^{2}$ at a certain point, and a second sound wave from a nearby ambulance has an intensity level $10 \mathrm{~dB}$ greater than the siren's sound wave at the same point. What is the intensity level of the sound wave due to the ambulance?

Prabhu Ramji

Numerade Educator

Problem 3

A person wears a hearing aid that uniformly increases the intensity level of all audible frequencies of sound by $30.0 \mathrm{~dB}$. The hearing aid picks up sound having a frequency of $250 \mathrm{~Hz}$ at an intensity of $3.0 \times 10^{-11} \mathrm{~W} / \mathrm{m}^{2}$. What is the intensity delivered to the eardrum?

Averell Hause

Carnegie Mellon University

Problem 3

The coldest recorded temperature of air on Earth, $-128.6^{\circ} \mathrm{F}$, occurred on July 21,1983 , at Vostok, a Russian station in Antarctica. What is the speed of sound in air at this temperature?

Prabhu Ramji

Numerade Educator

Problem 4

A dolphin located in seawater at a temperature of $25^{\circ} \mathrm{C}$ emits a sound directed toward the bottom of the ocean $150 \mathrm{~m}$ below. How much time passes before it hears an echo?

Patrick Connors

Patrick Connors

Numerade Educator

Problem 5

A group of hikers hears an echo $3.00 \mathrm{~s}$ after shouting. If the temperature is $22.0^{\circ} \mathrm{C}$, how far away is the mountain that reflected the sound wave?

Prabhu Ramji

Numerade Educator

Problem 6

The range of human hearing extends from approximately $20 \mathrm{~Hz}$ to $20000 \mathrm{~Hz}$. Find the wavelengths of these extremes at a temperature of $27^{\circ} \mathrm{C}$.

Patrick Connors

Patrick Connors

Numerade Educator

Problem 7

You are watching a pier being constructed on the far shore of a saltwater inlet when some blasting occurs. You hear the sound in the water $4.50 \mathrm{~s}$ before it reaches you through the air. How wide is the inlet? Hint: See Table 14.1. Assume the air temperature is $20^{\circ} \mathrm{C}$.

Prabhu Ramji

Numerade Educator

Problem 8

A stone is dropped from rest into a well. The sound of the splash is heard exactly $2.00 \mathrm{~s}$ later. Find the depth of the well if the air temperature is $10.0^{\circ} \mathrm{C}$.

Patrick Connors

Patrick Connors

Numerade Educator

Problem 9

A sound wave traveling in air at $65^{\circ} \mathrm{C}$ has a frequency of $845 \mathrm{~Hz}$. Find (a) the wave speed and (b) the wavelength.

Prabhu Ramji

Numerade Educator

Problem 10

The intensity level produced by a jet airplane at a certain location is $150 \mathrm{~dB}$. (a) Calculate the intensity of the sound wave generated by the jet at the given location.
(b) Compare the answer to part (a) to the threshold of pain and explain why employees directing jet airplanes at airports must wear hearing protection equipment.

Patrick Connors

Patrick Connors

Numerade Educator

Problem 11

One of the loudest sounds in recent history was that made by the explosion of Krakatoa on August $26-27,1883$. According to barometric measurements, the sound had a decibel level of $180 \mathrm{~dB}$ at a distance of $161 \mathrm{~km}$. Assuming the intensity falls off as the inverse of the distance squared, what was the decibel level on Rodriguez Island, $4800 \mathrm{~km}$ away?

Prabhu Ramji

Numerade Educator

Problem 14

The area of a typical eardrum is about $5.0 \times 10^{-5} \mathrm{~m}^{2}$. Calculate the sound power (the energy per second) incident on an eardrum at (a) the threshold of hearing and (b) the threshold of pain.

Patrick Connors

Patrick Connors

Numerade Educator

Problem 15

The toadfish makes use of resonance in a closed tube to produce very loud sounds. The tube is its swim bladder, used as an amplifier. The sound level of this creature has been measured as high as $100 \mathrm{~dB}$. (a) Calculate the intensity of the sound wave emitted. (b) What is the intensity level if three of these fish try to imitate three frogs by saying "Budweiser" at the same time?

Prabhu Ramji

Numerade Educator

Problem 16

A trumpet creates a sound intensity level of $1.15 \times$ $10^{2} \mathrm{~dB}$ at a distance of $1.00 \mathrm{~m}$. (a) What is the sound intensity of a trumpet at this distance? (b) What is the sound intensity of five trumpets at this distance? (c) Find the sound intensity of five trumpets at the location of the first row of an audience, $8.00 \mathrm{~m}$ away, assuming, for simplicity, the sound energy propagates uniformly in all directions. (d) Calculate the decibel level of the five trumpets in the first row. (e) If the trumpets are being played in an outdoor auditorium, how far away, in theory, can their combined sound be heard? (f) In practice such a sound could not be heard once the listener was $2-3 \mathrm{~km}$ away. Why can't the sound be heard at the distance found in part (e)? Hint: In a very quiet room the ambient sound intensity level is about $30 \mathrm{~dB}$.

Ahmed Shalaby

Numerade Educator

Problem 17

There is evidence that elephants communicate via infrasound, generating rumbling vocalizations as low as $14 \mathrm{~Hz}$ that can travel up to $10 \mathrm{~km}$. The intensity level of these sounds can reach $103 \mathrm{~dB}$, measured a distance of $5.0 \mathrm{~m}$ from the source. Determine the intensity level of the infrasound $10 \mathrm{~km}$ from the source, assuming the sound energy radiates uniformly in all directions.

Prabhu Ramji

Numerade Educator

Problem 18

A family ice show is held at an enclosed arena. The skaters perform to music playing at a level of $80.0 \mathrm{~dB}$. This intensity level is too loud for your baby, who yells at $75.0 \mathrm{~d} \mathrm{~B}$. (a) What total sound intensity engulfs you? (b) What is the combined sound level?

Patrick Connors

Patrick Connors

Numerade Educator

Problem 19

A train sounds its horn as it approaches an intersection. The horn can just be heard at a level of $50 \mathrm{~dB}$ by an observer $10 \mathrm{~km}$ away. (a) What is the average power generated by the horn? (b) What intensity level of the horn's sound is observed by someone waiting at an intersection $50 \mathrm{~m}$ from the train? Treat the horn as a point source and neglect any absorption of sound by the air.

Prabhu Ramji

Numerade Educator

Problem 20

An outside loudspeaker (considered a small source) emits sound waves with a power output of $100 \mathrm{~W}$. (a) Find the intensity $10.0 \mathrm{~m}$ from the source. (b) Find the intensity level in decibels at that distance. (c) At what distance would you experience the sound at the threshold of pain, $120 \mathrm{~dB} ?$

Patrick Connors

Patrick Connors

Numerade Educator

Problem 21

Show that the difference in decibel levels $\beta_{1}$ and $\beta_{2}$ of a sound source is related to the ratio of its distances $\bar{r}_{1}$ and $r_{0}$ from the receivers by the formula
$$\beta_{2}-\beta_{1}=20 \log \left(\frac{r_{1}}{r_{2}}\right)$$

Prabhu Ramji

Numerade Educator

Problem 22

A skyrocket explodes $100 \mathrm{~m}$ above the ground (Fig. P14.22). Three observers are spaced $100 \mathrm{~m}$ apart, with the first (A) directly under the explosion. (a) What is the ratio of the sound intensity heard by observer $A$ to that heard by observer B? (b) What is the ratio of the intensity heard be observer $A$ to that heard by observer C?

Patrick Connors

Patrick Connors

Numerade Educator

Problem 23

A commuter train passes a passenger platform at a constant speed of $40.0 \mathrm{~m} / \mathrm{s}$. The train horn is sounded at its characteristic frequency of $320 \mathrm{~Hz}$. (a) What overall change in frequency is detected by a person on the platform as the train moves from approaching to receding?
(b) What wavelength is detected by a person on the platform as the train approaches?

Averell Hause

Carnegie Mellon University

Problem 24

An airplane traveling at half the speed of sound $v=$ $172 \mathrm{~m} / \mathrm{s}$ ) emits a sound of frequency $5.00 \mathrm{kHz}$. At what frequency does a stationary listener hear the sound (a) as the plane approaches? (b) After it passes?

Prabhu Ramji

Numerade Educator

Problem 25

Two trains on separate tracks move toward each other. Train 1 has a speed of $130 \mathrm{~km} / \mathrm{h}$, train 2 a speed of $90.0 \mathrm{~km} / \mathrm{h}$. Train 2 blows its horn, emitting a frequency of $500 \mathrm{~Hz}$. What is the frequency heard by the engineer on train 1?

Prabhu Ramji

Numerade Educator

Problem 26

At rest, a car's horn sounds the note A $(440 \mathrm{~Hz})$. The horn is sounded while the car is moving down the street. A bicyclist moving in the same direction with one-third the car's speed hears a frequency of $415 \mathrm{~Hz}$. What is the speed of the car? Is the cyclist ahead of or behind the car?

Prabhu Ramji

Numerade Educator

Problem 27

An alert physics student stands beside the tracks as a train rolls slowly past. He notes that the frequency of the train whistle is $442 \mathrm{~Hz}$ when the train is approaching him and $441 \mathrm{~Hz}$ when the train is receding from him. Using these frequencies, he calculates the speed of the train. What value does he find?

Prabhu Ramji

Numerade Educator

Problem 28

A bat flying at $5.00 \mathrm{~m} / \mathrm{s}$ is chasing a insect flying in the same direction. If the bat emits a $40.0-\mathrm{kH}_{\mathrm{z}}$ chirp and receives back an echo at $40.4 \mathrm{kHz}$, what is the speed of the insect? (Take the speed of sound in air to be $340 \mathrm{~m} / \mathrm{s}$.)

Prabhu Ramji

Numerade Educator

Problem 29

A tuning fork vibrating at $512 \mathrm{~Hz}$ falls from rest and accelerates at $9.80 \mathrm{~m} / \mathrm{s}^{2}$. How far below the point of release is the tuning fork when waves of frequency $485 \mathrm{~Hz}$ reach the release point? Take the speed of sound in air to be $340 \mathrm{~m} / \mathrm{s}$.

Keshav Singh

Numerade Educator

Problem 30

Expectant parents are thrilled to hear their unborn baby's heartbeat, revealed by an ultrasonic motion detector. Suppose the fetus's ventricular wall moves in simple harmonic motion with amplitude $1.80 \mathrm{~mm}$ and frequency 115 per minute. (a) Find the maximum linear speed of the heart wall. Suppose the motion detector in contact with the mother's abdomen produces sound at precisely 2 MHz, which travels through tissue at $1.50 \mathrm{~km} / \mathrm{s}$.
(b) Find the maximum frequency at which sound arrives at the wall of the baby's heart. (c) Find the maximum frequency at which reflected sound is received by the motion detector. (By electronically "listening" for echoes at a frequency different from the broadcast frequency, the motion detector can produce beeps of audible sound in synchrony with the fetal heartbeat.)

Prabhu Ramji

Numerade Educator

Problem 31

The now-discontinued Concorde flew at Mach $1.5$, which meant that the speed of the plane was $1.5$ times the speed of sound in air. What was the angle between the direction of propagation of the shock wave and the direction of the plane's velocity?

Prabhu Ramji

Numerade Educator

Problem 32

A yellow submarine traveling horizontally at $11.0 \mathrm{~m} / \mathrm{s}$ uses sonar with a frequency of $5.27 \times 10^{3} \mathrm{~Hz}$. A red submarine is in front of the yellow submarine and moving $3.00 \mathrm{~m} / \mathrm{s}$ relative to the water in the same direction. A crewman in the red submarine observes sound waves ("pings") from the yellow submarine. Take the speed of sound in seawater as $1531 \mathrm{~m} / \mathrm{s}$. (a) Write Equation 14.12. (b) Which submarine is the source of the sound? (c) Which submarine carries the observer?
(d) Does the motion of the observer's submarine increase or decrease the time between the pressure maxima of the incoming sound waves? How does that affect the observed period? The observed frequency? (e) Should the sign of $v_{0}$ be positive or negative? (f) Does the motion of the source submarine increase or decrease the time observed between the pressure maxima? How does this motion affect the observed period? The observed frequency?
(g) What sign should be chosen for $v_{e}^{2}(\mathrm{~h})$ Substitute the appropriate numbers and obtain the frequency observed by the crewman on the red submarine.

Eduard Sanchez

Numerade Educator

Problem 33

A pair of speakers connected to the same sound system face each other, one at $x=0$ and the other at $x=4.00 \mathrm{~m}$. If they are playing a sound with frequency $343 \mathrm{~Hz}$, what are the points of constructive interference between the two speakers? (Take the speed of sound as $343 \mathrm{~m} / \mathrm{s}$.)

Prabhu Ramji

Numerade Educator

Problem 34

The acoustical system shown in Figure $14.14$ is driven by a speaker emitting sound of frequency $756 \mathrm{~Hz}$. (a) If constructive interference occurs at a particular instant, by what minimum amount should the path length in the upper U-shaped tube be increased so that destructive interference occurs instead? (b) What minimum increase in the original length of the upper tube will again result in constructive interference? Take the speed of sound as $345 \mathrm{~m} / \mathrm{s}$.

Prabhu Ramji

Numerade Educator

Problem 35

The ship in Figure $\mathrm{P} 14.35$ travels along a straight line parallel to the shore and $600 \mathrm{~m}$ from it. The ship's radio receives simultaneous signals of the same frequency from antennas $A$ and $B$. The signals interfere constructively at point $C$, which is equidistant from $A$ and $B$. The signal goes through the first minimum at point $D$. Determine the wavelength of the radio waves.

Prabhu Ramji

Numerade Educator

Problem 36

Two loudspeakers are placed above and below each other, as in Figure $14.15$, and driven by the same source at a frequency of $4.50 \times 10^{2} \mathrm{~Hz}$. An observer is in front of the speakers (to the right) at point $O$, at the same distance from each speaker. If the speed of sound is $345 \mathrm{~m} / \mathrm{s}$, what minimum vertical distance upward should the top speaker be moved to create destructive interference at point $O ?$

Prabhu Ramji

Numerade Educator

Problem 37

A pair of speakers separated by $0.700 \mathrm{~m}$ are driven by the same oscillator at a frequency of $690 \mathrm{~Hz}$. An observer originally positioned at one of the speakers begins to walk along a line perpendicular to the line joining the speakers. (a) How far must the observer walk before reaching a relative maximum in intensity? (b) How far will the observer be from the speaker when the first relative minimum is detected in the intensity?

Prabhu Ramji

Numerade Educator

Problem 38

A steel wire in a piano has a length of $0.7000 \mathrm{~m}$ and a mass of $4.300 \times 10^{-3} \mathrm{~kg}$. To what tension must this wire be stretched so that the fundamental vibration corresponds to middle $\mathrm{C}\left(f_{C}=261.6 \mathrm{~Hz}\right.$ on the chromatic musical scale)?

Patrick Connors

Patrick Connors

Numerade Educator

Problem 39

A stretched string fixed at each end has a mass of $40.0 \mathrm{~g}$ and a length of $8.00 \mathrm{~m}$. The tension in the string is $49.0 \mathrm{~N}$.
(a) Determine the positions of the nodes and antinodes for the third harmonic. (b) What is the vibration frequency for this harmonic?

Averell Hause

Carnegie Mellon University

Problem 40

Resonance of sound waves can be produced within an aluminum rod by holding the rod at its midpoint and stroking it with an alcohol-saturated paper towel. In this resonance mode, the middle of the rod is a node while the ends are antinodes; no other nodes or antinodes are present. What is the frequency of the resonance if the rod is $1.00 \mathrm{~m}$ long?

Prabhu Ramji

Numerade Educator

Problem 41

Two speakers are driven by a common oscillator at $800 \mathrm{~Hz}$ and face each other at a distance of $1.25 \mathrm{~m}$. Locate the points along a line joining the speakers where relative minima of the amplitude of the pressure would be expected. (Use $v=343 \mathrm{~m} / \mathrm{s}$.)

Prabhu Ramji

Numerade Educator

Problem 42

Two pieces of steel wire with identical cross sections have lengths of $L$ and $2 L$. The wires are each fixed at both ends and stretched so that the tension in the longer wire is four times greater than in the shorter wire. If the fundamental lrequency in the shorter wire is $60 \mathrm{~Hz}$, what is the frequency of the second harmonic in the longer wire?

Prabhu Ramji

Numerade Educator

Problem 43

A steel wire with mass $25.0 \mathrm{~g}$ and length $1.35 \mathrm{~m}$ is strung on a bass so that the distance from the nut to the bridge is $1.10 \mathrm{~m}$. (a) Compute the linear density of the string. (b) What velocity wave on the string will produce the desired fundamental frequency of the $\mathrm{E}_{1}$ string, $41.2 \mathrm{~Hz} ?$ (c) Calculate the tension required to obtain the proper frequency. (d) Calculate the wavelength of the string's vibration. (e) What is the wavelength of the sound produced in air? (Assume the speed of sound in air is $343 \mathrm{~m} / \mathrm{s}$.)

Prabhu Ramji

Numerade Educator

Problem 44

A standing wave is set up in a string of variable length and tension by a vibrator of variable frequency. Both ends of the string are fixed. When the vibrator has a frequency $\int_{A}$, in a string of length $L_{A}$ and under tension $T_{A}, n_{A}$ antinodes are set up in the string. (a) Write an expression for the frequency $f_{A}$ of a standing wave in terms of the number $n_{A}$, length $L_{d}$, tension $T_{A}$, and linear density $\mu_{i} \cdot$ (b) If the length of the string is doubled to $L_{l l}=2 L_{i}$, what frequency $f_{B}$ (written as a multiple of $f_{A}$ ) will result in the same number of antinodes? Assume the tension and linear density are unchanged. Hint: Make a ratio of expressions for $f_{B}$ and $f_{A}$. (c) If the frequency and length are held constant, what tension $T_{B}$ will produce $n_{A}+1$ antinodes? (d) If the frequency is tripled and the length of the string is halved. by what factor should the tension be changed so that twice as many antinodes are produced?

Eduard Sanchez

Numerade Educator

Problem 45

A $12-\mathrm{kg}$ object hangs in equilibrium from a string of total length $L=5.0 \mathrm{~m}$ and linear mass density $\mu=$ $0.0010 \mathrm{~kg} / \mathrm{m}$. The string is wrapped around two light, frictionless pulleys that are separated by the distance $d=$ $2.0 \mathrm{~m}$ (Fig. P14.45a). (a) Determine the tension in the string. (b) At what frequency must the string between the pulleys vibrate in order to form the standing-wave pattern shown in Figure $\mathrm{P} 14.45 \mathrm{~b}$ ?

Prabhu Ramji

Numerade Educator

Problem 46

In the arrangement shown in Figure $\mathrm{P} 14.46$, an object of mass $m=5.0 \mathrm{~kg}$ hangs from a cord around a light pulley. The length of the cord between point $P$ and the pulley is $L=2.0 \mathrm{~m}$, a) When the vibrator is set to a frequency of $150 \mathrm{~Hz}$, a standing wave with six loops is formed. What must be the linear mass density of the cord? (b) How many loops (if any) will result if $m$ is changed to $45 \mathrm{~kg}$ ? (c) How many loops (if any) will result if $m$ is changed to $10 \mathrm{~kg}^{2}$?

Prabhu Ramji

Numerade Educator

Problem 47

A $60.00-\mathrm{cm}$ guitar string under a tension of $50.000 \mathrm{~N}$ has a mass per unit length of $0.10000 \mathrm{~g} / \mathrm{cm}$. What is the highest resonant frequency that can be heard by a person capable of hearing frequencies up to $20000 \mathrm{~Hz} ?$

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 48

Standing-wave vibrations ate set ap in a crystal goblet with four nodes and four antinodes equally spaced around the $20.0-\mathrm{cm}$ circumference of its rim. If transverse waves move around the glass at $900 \mathrm{~m} / \mathrm{s}$, an opera singer would have to produce a high harmonic with what frequency in order to shatter the glass with a resonant vibration?

Prabhu Ramji

Numerade Educator

Problem 49

The windpipe of a typical whooping crane is about $5.0 \mathrm{ft}$. long. What is the lowest resonant frequency of this pipe, assuming it is closed at one end? Assume a temperature of $37^{\circ} \mathrm{C}$.

Averell Hause

Carnegie Mellon University

Problem 50

The overall length of a piccolo is $32.0 \mathrm{~cm}$. The resonating air column vibrates as in a pipe that is open at both ends. (a) Find the frequency of the lowest note a piccolo can play, assuming the speed of sound in air is $340 \mathrm{~m} / \mathrm{s}$. (b) Opening holes in the side effectively shortens the length of the resonant column. If the highest note a piccolo can sound is $4000 \mathrm{~Hz}$, find the distance between adjacent antinodes for this mode of vibration.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 51

The human ear canal is about $2.8 \mathrm{~cm}$ long. If it is regarded as a tube that is open at one end and closed at Lhe eardrum, what is the fundamental frequency around which we would expect hearing to be most sensitive? Take the speed of sound to be $340 \mathrm{~m} / \mathrm{s}$.

Prabhu Ramji

Numerade Educator

Problem 52

A tunnel under a river is $2.00 \mathrm{~km}$ long. (a) At what frequencies can the air in the tunnel resonate? (b) Explain whether it would be good to make a rule against blowing your car horn when you are in the tunnel.

Patrick Connors

Patrick Connors

Numerade Educator

Problem 53

A pipe open at both ends has a fundamental frequency of $300 \mathrm{~Hz}$ when the temperature is $0{ }^{\circ} \mathrm{C}$. (a) What is the length of the pipe? (b) What is the fundamental frequency at a temperature of $30^{\circ} \mathrm{C}$ ?

Prabhu Ramji

Numerade Educator

Problem 54

Two adjacent natural frequencies of an organ pipe are found to be $550 \mathrm{~Hz}$ and $650 \mathrm{~Hz}$. Calculate the fundamenLal frequency and length of this pipe. (Use $v=340 \mathrm{~m} / \mathrm{s}$.) Determine whether the pipe is open at both ends or open at only one end.

Prabhu Ramji

Numerade Educator

Problem 55

In certain ranges of a piano keyboard, more than one string is tuned to the same note to provide extra loudness. For example, the note at $1.10 \times 10^{2} \mathrm{~Hz}$ has two strings at this frequency. If one string slips from its normal tension of $6.00 \times 10^{2} \mathrm{~N}$ to $5.40 \times 10^{2} \mathrm{~N}$, what beat frequency is heard when the hammer strikes the two strings simultaneously?

Averell Hause

Carnegie Mellon University

Problem 56

The G string on a violin has a fundamental frequency of $196 \mathrm{H} z$. It is $30.0 \mathrm{~cm}$ long and has a mass of $0.500 \mathrm{~g}$. While this string is sounding, a nearby violinist effectively shortens the $G$ string on her identical violin (by sliding her finger down the string) until a beat frequency of $2.00 \mathrm{~Hz}$ is heard between the two strings. When that occurs, what is the effective length of her string?

Prabhu Ramji

Numerade Educator

Problem 57

Two train whistles have identical frequencies of $1.80 \times$ $10^{2} \mathrm{~Hz}$. When one train is at rest in the station and the other is moving nearby, a commuter standing on the station platform hears beats with a frequency of $2.00$ beats $/ \mathrm{s}$ when the whistles operate together. If the speed of sound is $345 \mathrm{~m} / \mathrm{s}$, what are the two possible speeds and directions that the moving train can have?

Prabhu Ramji

Numerade Educator

Problem 58

Two pipes of equal length are each open at one end. Each has a fundamental frequency of $480 \mathrm{~Hz}$ at $300 \mathrm{~K} .$ In one pipe the air temperature is increased to $305 \mathrm{~K}$. If the two pipes are sounded together, what beat frequency results?

Patrick Connors

Patrick Connors

Numerade Educator

Problem 59

A student holds a tuning fork oscillating at $256 \mathrm{~Hz}$. He walks toward a wall at a constant speed of $1.33 \mathrm{~m} / \mathrm{s}$.
(a) What beat frequency does he observe between the tuning fork and its echo? (b) How fast must he walk away from the wall to observe a beat frequency of $5.00 \mathrm{~Hz}$ ?

Mark Mathison

Numerade Educator

Problem 60

If a human ear canal can be thought of as resembling an organ pipe, closed at one end, that resonates at a fundamental frequency of $3000 \mathrm{~Hz}$, what is the length of the canal? Use a normal body temperature of $37^{\circ} \mathrm{C}$ for your determination of the speed of sound in the canal.

Sarah Mccrumb

Numerade Educator

Problem 61

Some studies suggest that the upper frequency limit of hearing is determined by the diameter of the eardrum. The wavelength of the sound wave and the diameter of the eardrum are approximately equal at this upper limit. If the relationship holds exactly, what is the diameter of the eardrum of a person capable of hearing $20000 \mathrm{~Hz}$ ? (Assume a body temperature of $37^{\circ} \mathrm{C}$.)

Sarah Mccrumb

Numerade Educator

Problem 62

The intensity level of an orchestra is $85 \mathrm{~dB}$. A single violin reaches a level of $7.0 \times 10^{1} \mathrm{~d} \mathrm{~B}$. What is the ratio of the sound intensity of the full orchestra to the intensity of a single violin?

Prabhu Ramji

Numerade Educator

Problem 63

Assume a loudspeaker broadcasts sound equally in all directions and produces sound with a level of $103 \mathrm{~dB}$ at a distance of $1.60 \mathrm{~m}$ from its center. (a) Find the loudspeaker's sound power output. (b) If a salesperson claims to be giving you $150 \mathrm{~W}$ per channel, she is referring to the electrical power input to the speaker. Find the efficiency of the speaker, that is, the fraction of input power that is converted into useful output power.

Prabhu Ramji

Numerade Educator

Problem 64

Two small loudspeakers emit sound waves of different frequencies equally in all directions, Speaker $A$ has an output of $1.00 \mathrm{~mW}$, and speaker $B$ has an output of $1.50 \mathrm{~mW}$. Determine the sound level (in decibels) at point $C$ in Figure $\mathrm{P} 14.64$ assuming (a) only speaker $A$ emits sound,
(b) only speaker $B$ emits sound, and (c) both speakers emit sound.

Patrick Connors

Patrick Connors

Numerade Educator

Problem 65

An interstate highway has been built though a poor neighborhood in a city. In the afternoon, the sound level in a rented room is $80.0 \mathrm{~dB}$ as 100 cars pass outside the window every minute. Late at night, the traffic flow is only five cars per minute. What is the average late-night sound level?

Prabhu Ramji

Numerade Educator

Problem 66

A student uses an audio oscillator of adjustable frequency to measure the depth of a water well. He reports hearing two successive resonances at $52.0 \mathrm{~Hz}$ and $60.0 \mathrm{~Hz}$. If the speed of sound is $345 \mathrm{~m} / \mathrm{s}$, how deep is the well?

Prabhu Ramji

Numerade Educator

Problem 67

When at rest, two trains have sirens that emit a frequency of $300 \mathrm{~Hz}$. The trains travel toward each other and toward an observer stationed between them. One of the trains moves at $30.0 \mathrm{~m} / \mathrm{s}$, and the observer hears a beat frequency of $3.0$ beats per second. What is the speed of the second train, which travels faster than $30.0 \mathrm{~m} / \mathrm{s}$ ?

Prabhu Ramji

Numerade Educator

Problem 68

A commuter train blows its horn as it passes a passenger platform at a constant speed of $40.0 \mathrm{~m} / \mathrm{s}$. The horn sounds at a frequency of $320 \mathrm{~Hz}$ when the train is at rest. What is the frequency observed by a person on the platform (a) as the train approaches and
(b) as the train recedes from him? (c) What wavelength does the observer find in each case?

Prabhu Ramji

Numerade Educator

Problem 69

A quartz watch contains a crystal oscillator in the form of a block of quartz that vibrates by contracting and expanding. Two opposite faces of the block, $7.05 \mathrm{~mm}$ apart, are antinodes, moving alternately toward and away from each other. The plane halfway between these two faces is a node of the vibration. The speed of sound in quartz is $3.70 \mathrm{~km} / \mathrm{s}$. Find the frequency of the vibration. An oscillating electric voltage accompanies the mechanical oscillation, so the quartz is described as piezoelectric. An electric circuit feeds in energy to maintain the oscillation and also counts the voltage pulses to keep time.

Jonathan Ibarra

Jonathan Ibarra

Numerade Educator

Problem 70

A flowerpot is knocked off a balcony $20.0 \mathrm{~m}$ above the sidewalk and falls toward an unsuspecting $1.75$ -m-tall man who is standing below. How close to the sidewalk can the flowerpot fall before it is too late for a warning shouted from the balcony to reach the man in time? Assume the man below requires $0.300 \mathrm{~s}$ to respond to the warning.

Prabhu Ramji

Numerade Educator

Problem 71

On a workday, the average decibel level of a busy street is $70 \mathrm{~dB}$, with 100 cars passing a given point every minute. If the number of cars is reduced to 25 every minute on a weekend, what is the decibel level of the street?

Averell Hause

Carnegie Mellon University

Problem 72

A flute is designed so that it plays a frequency of $261.6 \mathrm{~Hz}$. middle $C$, when all the holes are covered and the temperature is $20.0^{\circ} \mathrm{C}$. (a) Consider the flute to be a pipe open at both ends and find its length, assuming the middle-C.frequency is the fundamental frequency. (b) A second player, nearby in a colder room, also attempts to play middle $\mathrm{C}$ on an identical flute. A beat frequency of $3.00$ beats/s is heard. What is the temperature of the room?

Patrick Connors

Patrick Connors

Numerade Educator

Problem 73

A block with a speaker bolted to it is connected to a spring having spring constant $k=20.0 \mathrm{~N} / \mathrm{m}$, as shown in Figure P14.73. The total mass of the block and speaker is $5.00 \mathrm{~kg}$, and the amplitude of the unit's motion is $0.500 \mathrm{~m}$. If the speaker emits sound waves of frequency $440 \mathrm{~Hz}$, determine the lowest and highest frequencies heard by the person to the right of the speaker.

Prabhu Ramji

Numerade Educator

Problem 74

A student stands several meters in front of a smooth reflecting wall, holding a board on which a wire is fixed at each end. The wire, vibrating in its third harmonic, is $75.0 \mathrm{~cm}$ long, has a mass of $2.25 \mathrm{~g}$, and is under a tension of $400 \mathrm{~N}$. A second student, moving towards the wall. hears $8.30$ beats per second. What is the speed of the student approaching the wall? Use $340 \mathrm{~m} / \mathrm{s}$ as the speed of sound in air.

Prabhu Ramji

Numerade Educator

Problem 75

By proper excitation, it is possible to produce both longitudinal and transverse waves in a long metal rod. In a particular case, the rod is $150 \mathrm{~cm}$ long and $0.200 \mathrm{~cm}$ in radius and has a mass of $50.9 \mathrm{~g}$. Young's modulus for the material is $6.80 \times 10^{10} \mathrm{~Pa}$. Determine the required tension in the rod so that the ratio of the speed of longitudinal waves to the speed of transverse waves is 8 .

Prabhu Ramji

Numerade Educator