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# College Physics 2017

## Educators

AS

### Problem 1

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

Averell H.
Carnegie Mellon University

### Problem 2

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

Patrick C.

### Problem 3

On a hot summer day, the temperature of air in Arizona reaches $114^{\circ} \mathrm{F}$ . What is the speed of sound in air at this temperature?

Averell H.
Carnegie Mellon University

### 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 C.

### Problem 5

A group of hikers hears an echo 3.00 s after shouting. How far away is the mountain that reflected the sound wave?

Averell H.
Carnegie Mellon University

### 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 C.

### Problem 7

Calculate the reflected percentage of an ultrasound wave passing from human muscle into bone. Muscle has a typical density of $1.06 \times 10^{3} \mathrm{kg} / \mathrm{m}^{3}$ and bone has a typical density of $1.90 \times 10^{3} \mathrm{kg} / \mathrm{m}^{3}$

Averell H.
Carnegie Mellon University

### Problem 8

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

Patrick C.

### Problem 9

A hammer strikes one end of a thick steel rail of length 8.50 m. A microphone located at the opposite end of the rail detects two pulses of sound, one that travels through the air and a longitudinal wave that travels through the rail.
(a) Which pulse reaches the microphone first?
(b) Find the separation in time between the arrivals of the two pulses.

Averell H.
Carnegie Mellon University

### Problem 10

A person standing 1.00 $\mathrm{m}$ from a portable speaker hears its sound at an intensity of $7.50 \times 10^{-3} \mathrm{W} / \mathrm{m}^{2} .$ (a) Find the corresponding decibel level. (b) Find the sound intensity at a distance of $35.0 \mathrm{m},$ assuming the sound propagates as a spherical
wave. (c) Find the decibel level at a distance of 35.0 $\mathrm{m} .$

Patrick C.

### Problem 11

The mating call of a male cicada is among the loudest noises in the insect world, reaching decibel levels of 105 dB at a distance of 1.00 m from the insect. (a) Calculate the corresponding sound intensity. (b) Calculate the sound intensity at a distance of 20.0 m from the insect, assuming the sound
propagates as a spherical wave. (c) Calculate the decibel level at a distance of 20.0 m from 100 male cicadas each producing the same sound intensity.

Averell H.
Carnegie Mellon University

### Problem 12

The intensity level produced by a jet airplane at a certain location is 150 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 C.

### Problem 13

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 dB at a distance of 161 km. Assuming the intensity falls off as the inverse of the distance squared, what was the
decibel level on Rodriguez Island, 4 800 km away?

Averell H.
Carnegie Mellon University

### Problem 14

A sound wave from a siren has an intensity 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?

Patrick C.

### Problem 15

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

Averell H.
Carnegie Mellon University

### Problem 16

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 C.

### Problem 17

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. dB. (a) Calculate the intensity of the sound wave emitted. (b) What is the intensity level if three of these toadfish try to make a sound at the same time?

Averell H.
Carnegie Mellon University

### Problem 18

A trumpet creates a sound intensity level of $1.15 \times 10^{2}$ dB at a distance of 1.00 $\mathrm{m} .$ (b) 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 $\mathrm{dB}$ .

AS
Ahmed S.

### Problem 19

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

Averell H.
Carnegie Mellon University

### Problem 20

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

Patrick C.

### Problem 21

A train sounds its horn as it approaches an intersection. The horn can just be heard at a level of 50. dB by an observer 10 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. m from the train? Treat the horn as a point source and neglect any absorption of sound by the air.

Averell H.
Carnegie Mellon University

### Problem 22

An outside loudspeaker (considered a small source) emits sound waves with a power output of 100 W. (a) Find the intensity 10.0 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 dB?

Patrick C.

### Problem 23

Show that the difference in decibel levels $\beta_{1}$ and $\beta_{2}$ of a sound source is related to the ratio of its distances $r_{1}$ and $r_{2}$ from the receivers by the formula

$$\beta_{2}-\beta_{1}=20 \log \left(\frac{r_{1}}{r_{2}}\right)$$

Averell H.
Carnegie Mellon University

### Problem 24

A skyrocket explodes 100 $\mathrm{m}$ above the ground (Fig. $\mathrm{P} 14.24 )$
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 $\mathrm{A}$ to that heard by observer $\mathrm{B} ?$
(b) What is the ratio of the intensity heard by observer A to
that heard by observer $\mathrm{C}$ ?

Patrick C.

### Problem 25

A baseball hits a car, breaking its window and triggering its alarm which sounds at a frequency of 1250 $\mathrm{Hz}$ . What frequency is heard by a boy on a bicycle riding away from the car at 6.50 $\mathrm{m} / \mathrm{s}$ ?

Averell H.
Carnegie Mellon University

### Problem 26

A train is moving past a crossing where cars are waiting for it to pass. While waiting, the driver of the lead car becomes sleepy and rests his head on the steering wheel, unintentionally activating the car’s horn. A passenger in the back of the train hears the horn’s sound at a frequency of 428 Hz and a
passenger in the front hears it at 402 Hz. Find (a) the train’s speed and (b) the horn’s frequency, assuming the sound travels along the tracks.

Patrick C.

### Problem 27

A commuter train passes a passenger platform at a constant speed of 40.0 m/s. The train horn is sounded at its characteristic frequency of 320. 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 H.
Carnegie Mellon University

### Problem 28

An airplane traveling at half the speed of sound 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?

Patrick C.

### Problem 29

Two trains on separate tracks move toward each other. Train 1 has a speed of $1.30 \times 10^{2} \mathrm{km} / \mathrm{h} ;$ train $2,$ a speed of 90.0 $\mathrm{km} / \mathrm{h}$ . Train 2 blows its horn, emitting a frequency of $5.00 \times 10^{2} \mathrm{Hz}$ . What is the frequency heard by the engineer on train 1 ?

Averell H.
Carnegie Mellon University

### Problem 30

At rest, a car's horn sounds the note $\mathrm{A}(440 \mathrm{Hz}) .$ 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 Hz. (a) Is the cyclist ahead of or behind the car? (b) What is the speed of the car?

Patrick C.

### Problem 31

An alert physics student stands beside the tracks as a train rolls slowly past. He notes that the frequency of the train whistle is 465 Hz when the train is approaching him and 441 Hz when
the train is receding from him. Using these frequencies, he calculates the speed of the train. What value does he find?

Averell H.
Carnegie Mellon University

### Problem 32

A bat flying at 5.00 m/s is chasing an insect flying in the same direction. If the bat emits a 40.0-kHz chirp and receives back an echo at 40.4 kHz, (a) what is the speed of the insect? (b) Will the bat be able to catch the insect? Explain.

Patrick C.

### Problem 33

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?

Averell H.
Carnegie Mellon University

### Problem 34

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 mm and frequency 115 beats per minute. The motion detector in contact with the mother's abdomen produces sound at precisely 2 $\mathrm{MHz}$ , which travels through tissue at 1.50 $\mathrm{km} / \mathrm{s}$ . (a) Find the maximum linear speed of the heart wall. (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.)

Patrick C.

### Problem 35

A supersonic jet traveling at Mach 3.00 at an altitude of $h=2.00 \times 10^{4} \mathrm{m}$ is directly over a person at time $t=0$ as shown in Figure $\mathrm{P} 14.35$ . Assume the average speed of sound in air is 335 $\mathrm{m} / \mathrm{s}$ over the path of the sound. (a) At what time will the person encounter the shock wave due to the sound emitted at $t=0$ ? (b) Where will the plane be when this shock wave is heard?

Averell H.
Carnegie Mellon University

### Problem 36

A yellow submarine traveling horizontally at 11.0 m/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 m/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 1 533 m/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 $v_{s}^{2}(\mathrm{h})$ Substitute the appropriate numbers and obtain the frequency observed by the crewman on the red submarine.

Patrick C.

### Problem 37

Two cars are stuck in a traffic jam and each sounds its horn at a frequency of 625 Hz. A bicyclist between the two cars, 4.50 m from each horn (Fig. P14.37), is disturbed to find she is at a point of constructive interference. How far backward must she move to reach the nearest point of destructive interference?

Averell H.
Carnegie Mellon University

### Problem 38

The acoustical system shown in Figure P14.38 is driven by a speaker emitting sound of frequency 756 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?

Patrick C.

### Problem 39

The ship in Figure P14.39 travels along a straight line parallel to the shore and a distance d 5 600 m from it. The ship’s radio receives simultaneous signals of the same frequency from antennas A and B, separated by a distance L 5 800 m. The signals interfere constructively at point C, which is equidistant from A and B. The signal goes through the first minimum at point D, which is directly outward from the shore from point B. Determine the wave-length of the radio waves.

Averell H.
Carnegie Mellon University

### Problem 40

Two loudspeakers are placed above and below each other, as in Figure $\mathrm{P} 14.40$ 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. What minimum vertical distance upward should the top speaker be moved to create destructive interference at point O?

Patrick C.

### Problem 41

A pair of speakers separated by a distance d 5 0.700 m are driven by the same oscillator at a frequency of 686 Hz. An observer originally positioned at one of the speakers begins to walk along a line perpendicular to the line joining the speakers as in Figure P14.41. (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?

Averell H.
Carnegie Mellon University

### Problem 42

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 $\mathrm{C}\left(f_{C}=261.6 \mathrm{Hz} \text { on the chromatic musical scale)? }\right.$

Patrick C.

### Problem 43

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

Averell H.
Carnegie Mellon University

### Problem 44

How far, and in what direction, should a cellist move her finger to adjust a string’s tone from an out - of - tune 449 Hz to an in - tune 440 Hz? The string is 68.0 cm long, and the finger is 20.0 cm from the nut for the 449-Hz tone.

Patrick C.

### Problem 45

A stretched string of length L is observed to vibrate in five equal segments when driven by a 630.-Hz oscillator. What oscillator frequency will set up a standing wave so that the string vibrates in three segments?

Averell H.
Carnegie Mellon University

### Problem 46

A distance of 5.00 cm is measured between two adjacent nodes of a standing wave on a 20.0 - cm - long string. (a) In which harmonic number n is the string vibrating? (b) Find the frequency of this harmonic if the string has a mass of $1.75 \times 10^{-2}$ kg and a tension of 875 $\mathrm{N}$ .

Patrick C.

### Problem 47

A steel wire with mass 25.0 g and length 1.35 m is strung on a bass so that the distance from the nut to the bridge is 1.10 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 wave-length of the sound produced in air? (Assume the speed of sound in air is 343 $\mathrm{m} / \mathrm{s} . )$

Averell H.
Carnegie Mellon University

### Problem 48

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 $f_{A},$ in a string of length $L_{A}$ and under tension $T_{A}, n_{A}$ anti-nodes 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 $L_{A},$ tension $T_{A},$ and linear density $\mu_{A} .$ If the length of the string is doubled to $L_{B}=2 L_{A},$ what frequency $f_{B}\left(\text { written as a multiple of } f_{A}\right)$ 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 anti-nodes are produced?

Patrick C.

### Problem 49

A 12.0 -kg object hangs in equilibrium from a string with total length of $L=5.00 \mathrm{m}$ and linear mass density of $\mu=0.00100$ kg/m. The string is wrapped around two light, frictionless pulleys that are separated by the distance d 5 2.00 m (Fig. P14.49a). (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 P14.49b?

Averell H.
Carnegie Mellon University

### Problem 50

In the arrangement shown in Figure P14.50, an object of mass m 5 5.0 kg hangs from a cord around a light pulley. The length of the cord between point P and the pulley is L 5 2.0 m. (a) When the vibrator is set to a frequency of 150 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 kg? (c) How many loops (if any) will result if m is changed to 10 kg?

Patrick C.

### Problem 51

A 60.00 - cm guitar string under a tension of 50.000 N has a mass per unit length of 0.100 00 g/cm. What is the highest resonant frequency that can be heard by a person capable of hearing frequencies up to 20 000 Hz?

Averell H.
Carnegie Mellon University

### Problem 52

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

Patrick C.

### Problem 53

A car's 30.0 -kg front tire is suspended by a spring with spring constant $k=1.00 \times 10^{5} \mathrm{N} / \mathrm{m} .$ At what speed is the car moving if washboard bumps on the road every 0.750 $\mathrm{m}$ drive the tire into a resonant oscillation?

Averell H.
Carnegie Mellon University

### Problem 54

A pipe has a length of 0.750 m and is open at both ends. (a) Calculate the two lowest harmonics of the pipe. (b) Calculate the two lowest harmonics after one end of the pipe is closed.

Patrick C.

### Problem 55

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 H.
Carnegie Mellon University

### Problem 56

The overall length of a piccolo is 32.0 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. (b) Opening holes in the side effectively shortens the length of the resonant column. If the highest note a piccolo can sound is $4.00 \times 10^{3} \mathrm{Hz}$ , find the distance between adjacent antinodes for this mode of vibration.

Patrick C.

### Problem 57

The human ear canal is about 2.8 cm long. If it is regarded as a tube that is open at one end and closed at the eardrum, what is the fundamental frequency around which we would expect hearing to be most sensitive?

Averell H.
Carnegie Mellon University

### Problem 58

A tunnel under a river is 2.00 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 C.

### Problem 59

A pipe open at both ends has a fundamental frequency of $3.00 \times 10^{2} \mathrm{Hz}$ 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 $30.0^{\circ} \mathrm{C}$ ?

Averell H.
Carnegie Mellon University

### Problem 60

Two adjacent natural frequencies of an organ pipe are found to be 550. Hz and 650. Hz. (a) Calculate the fundamental frequency of the pipe. (b) Is the pipe open at both ends or open at only one end? (c) What is the length of the pipe?

Patrick C.

### Problem 61

A guitarist sounds a tuner at 196 Hz while his guitar sounds a frequency of 199 Hz. Find the beat frequency.

Averell H.
Carnegie Mellon University

### Problem 62

Two nearby trumpets are sounded together and a beat frequency of 2 Hz is heard. If one of the trumpets sounds at a frequency of 525 Hz, what are the two possible frequencies of the other trumpet?

Patrick C.

### Problem 63

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 H.
Carnegie Mellon University

### Problem 64

The G string on a violin has a fundamental frequency of 196 Hz. It is 30.0 cm long and has a mass of 0.500 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 Hz is heard between the two strings. When that occurs, what is the effective length of her string?

Patrick C.

### Problem 65

Two train whistles have identical frequencies of $1.80 \times 10^{2}$ 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/s when the whistles operate together. What are the two possible speeds and directions that the moving train can have?

Patrick C.

### Problem 66

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

Patrick C.

### Problem 67

A student holds a tuning fork oscillating at 256 Hz. He walks toward a wall at a constant speed of 1.33 m/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 Hz?

Patrick C.

### Problem 68

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 $3.0 \times 10^{3} \mathrm{Hz}$ , what is the length of the canal? Use
a normal body temperature of $37.0^{\circ} \mathrm{C}$ for your determination of the speed of sound in the canal.

Patrick C.

### Problem 69

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 $2.00 \times 10^{4}$ Hz? (Assume a body temperature of $37.0^{\circ} \mathrm{C} .$ )

Averell H.
Carnegie Mellon University

### Problem 70

A typical sound level for a buzzing mosquito is 40 dB, and that of a vacuum cleaner is approximately 70 dB. Approximately how many buzzing mosquitoes will produce a sound intensity equal to that of a vacuum cleaner?

Patrick C.

### Problem 71

Assume a 150. - W loudspeaker broadcasts sound equally in all directions and produces sound with a level of 103 dB at a distance of 1.60 m from its center. (a) Find its sound power output. If a salesperson claims the speaker is rated at 150. W, he is referring to the maximum electrical power input to the
speaker. (b) Find the efficiency of the speaker, that is, the fraction of input power that is converted into useful output power.

Averell H.
Carnegie Mellon University

### Problem 72

Two small loudspeakers emit sound waves of different frequencies equally in all directions. Speaker A has an output of 1.00 mW, and speaker B has an output of 1.50 mW. Determine the sound level (in decibels) at point C in Figure P14.72 assuming (a) only speaker A emits sound, (b) only speaker B emits sound, and (c) both speakers emit sound.

Patrick C.

### Problem 73

An interstate highway has been built through a neighborhood in a city. In the afternoon, the sound level in an apartment in the neighborhood is 80.0 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?

Averell H.
Carnegie Mellon University

### Problem 74

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 Hz and 60.0 Hz. How deep is the well?

Patrick C.

### Problem 75

A stereo speaker is placed between two observers who are 36.0 m apart, along the line connecting them. If one observer records an intensity level of 60.0 dB, and the other records an intensity level of 80.0 dB, how far is the speaker from each observer?

Averell H.
Carnegie Mellon University

### Problem 76

Two ships are moving along a line due east (Fig. P14.76). The trailing vessel has a speed relative to a land-based observation point of $v_{1}=64.0 \mathrm{km} / \mathrm{h}$ , and the leading ship has a speed of $v_{2}=45.0 \mathrm{km} / \mathrm{h}$ relative to that point. The two ships are in a region of the ocean where the current is moving uniformly due west at $v_{\text { cument }}=10.0 \mathrm{km} / \mathrm{h}$ . The trailing ship transmits a sonar signal at a frequency of 1200.0 $\mathrm{Hz}$ through the water. What frequency is monitored by the leading ship?

Patrick C.

### Problem 77

On a workday, the average decibel level of a busy street is 70.0 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 H.
Carnegie Mellon University

### Problem 78

A flute is designed so that it plays a frequency of 261.6 $\mathrm{Hz}$ , middle $\mathrm{C}$ , 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 C on an identical
flute. A beat frequency of 3.00 beats/s is heard. What is the temperature of the room?

Patrick C.

### Problem 79

A block with a speaker bolted to it is connected to a spring having spring constant k 5 20.0 N/m, as shown in Figure P14.79. The total mass of the block and speaker is 5.00 kg, and the amplitude of the unit’s motion is 0.500 m. If the speaker emits sound waves of frequency 440. Hz, determine the (a) lowest and (b) highest frequencies heard by the person to the right of the speaker.

Averell H.
Carnegie Mellon University

### Problem 80

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 cm long, has a mass of 2.25 g, and is under a tension of 400. N. A second student, moving toward the wall, hears 8.30 beats per second. What is the speed of the student approaching the wall?

Patrick C.

### Problem 81

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 1.50 m long and 0.200 cm in radius and has a mass of 50.9 g. Young's modulus for the material is $6.80 \times$ $10^{10}$ Pa. Determine the required tension in the rod so that the ratio of the speed of longitudinal waves to the speed of trans-verse waves is $8 .$

Averell H.
Carnegie Mellon University

### Problem 82

A 0.500 - m - long brass pipe open at both ends has a fundamental frequency of 350. Hz. (a) Determine the temperature of the air in the pipe. (b) If the temperature is increased by $20.0^{\circ} \mathrm{C},$ what is the new fundamental frequency of the pipe? Be sure to include the effects of temperature on both the speed of sound in air and the length of the pipe.

Patrick C.