Deck 17: Waves in Two and Three Dimensions

Question 1

A transverse wave traveling along a string transports energy at a rate r.If we want to double this rate,we could

A) increase the amplitude of the wave by a factor of 8.
B) increase the amplitude of the wave by a factor of 4.
C) increase the amplitude of the wave by a factor of 2.
D) increase the amplitude by a factor of
E) increase the amplitude by a factor of

Answer 1

increase the amplitude by a factor of

Question 2

A stationary siren emits sound of frequency 1000 Hz and wavelength 0.343 m.An observer who is moving toward the siren will measure a frequency f and wavelength λ for this sound such that

A) f > 1000 Hz and λ > 0.343 m.
B) f > 1000 Hz and λ = 0.343 m.
C) f > 1000 Hz and λ < 0.343 m.
D) f = 1000 Hz and λ < 0.343 m.

Answer 2

f > 1000 Hz and λ = 0.343 m.

Question 3

The sound level at 1.0 m from a certain talking person talking is 60 dB.You are surrounded by five such people,all 1.0 m from you and all talking equally loud at the same time.The threshold of hearing is 1.0 × 10^-12 W/m².What sound level are you being exposed to? You can neglect any absorption,reflection,or interference of the sound.The threshold of hearing is 1.0 × 10^-12 W/m².

A) 300 dB
B) 60 dB
C) 74 dB
D) 67 dB
E) 81 dB

Answer 3

67 dB

Question 4

A tiny vibrating source sends waves uniformly in all directions.An area of 3.25 cm² on a sphere of radius 2.50 m centered on the source receives energy at a rate of 4.20 J/s.
(a)What is the intensity of the waves at 2.50 m from the source and at 10.0 m from the source?
(b)At what rate is energy leaving the vibrating source of the waves?

Question 5

Two people are talking at a distance of 3.0 m from where you are and you measure the sound intensity as 1.1 × 10^-7 W/m².Another student is 4.0 m away from the talkers.What sound intensity does the other student measure? Assume that the sound spreads out uniformly and undergoes no significant reflections or absorption.

A) 6.2 × 10^-8 W/m²
B) 1.5 × 10^-7 W/m²
C) 8.3 × 10^-8 W/m²
D) 7.8 × 10^-7 W/m²
E) 2.5 × 10^-8 W/m²

Question 6

A sound source emits 20.0 W of acoustical power spread equally in all directions.The threshold of hearing is 1.0 × 10^-12 W/m².What is the sound intensity level 30.0 m from the source?

A) 92.5 dB
B) 81.5 dB
C) 1.77 × 10^-3 dB
D) 1.77 × 10^-3 W
E) -27.5 dB

Question 7

A howler monkey is the loudest land animal and,under some circumstances,can be heard up to a distance of 5.0 km.Assume the acoustic output of a howler to be uniform in all directions and that the threshold of hearing is 1.0 × 10^-12 W/m².The acoustic power emitted by the howler is closest to

A) 0.31 mW.
B) 0.11 mW.
C) 1.1 mW.
D) 3.2 mW.
E) 11 mW.

Question 8

Two pure tones are sounded together and a particular beat frequency is heard.What happens to the beat frequency if the frequency of one of the tones is increased?

A) It increases.
B) It decreases.
C) It does not change.
D) It becomes zero.
E) We cannot tell from the information given.

Question 9

Which one of the following statements is true?

A) Both the intensity level (in dB) and the sound intensity can never be negative.
B) The intensity level (in dB) obeys an inverse-square distance law, but the sound intensity does not.
C) Both intensity level (in dB) and sound intensity obey inverse-square distance laws.
D) The sound intensity can never be negative, but the intensity level (in dB) can be negative.
E) Both the intensity level (in dB) and the sound intensity can be negative.

Question 10

What characteristic of sound determines the "pitch" of a musical note?

A) amplitude
B) wavelength
C) frequency
D) phase
E) intensity

Question 11

Calculate the light intensity 1.51 m from a light bulb that emits 100 W of visible light,assuming that the light radiates uniformly in all directions.

A) 3.49 W/m²
B) 4.01 W/m²
C) 43.9 W/m²
D) 50.5 W/m²

Question 12

Observer A is 3.0 m from a tiny light bulb and observer B is 12.0 m from the same bulb.Assume that the light spreads out uniformly and undergoes no significant reflections or absorption.If observer B sees a light of intensity I,the light intensity that A sees is

A) I.
B) 9I.
C) 16I.
D) 36I.
E) 144I.

Question 13

Shock waves occur when

A) the frequency of the waves is the resonant frequency of the system.
B) the amplitude of waves exceeds the critical shock value.
C) two waves from different sources collide with each other.
D) the wave source is traveling at a speed greater than the wave speed.
E) the period of the waves matches the lifetime of the waves.

Question 14

A certain source of sound waves radiates uniformly in all directions.At a distance of 20 m from the source the intensity level is 51 db.What is the total acoustic power output of the source,in watts?
(Note: The reference intensity I₀ is 1.0 × 10^-12 W/m².)

Question 15

A plane flies toward a stationary siren at 1/4 the speed of sound.Then the plane stands still on the ground and the siren is driven toward it at 1/4 the speed of sound.In both cases,a person sitting in the plane will hear the same frequency of sound from the siren.

Question 16

The intensity of sunlight falling on the earth is about 1.4 kW/m² (before any gets absorbed by our atmosphere).At what rate does the sun emit light energy? (The earth-sun distance = 1.5 × 10⁸ km and the earth's radius = 6.4 × 10³ km.)

A) 4.0 × 10²⁶ W
B) 3.2 × 10²² W
C) 7.2 × 10¹⁴ W
D) 7.6 × 10⁸ W

Question 17

The howler monkey is the loudest land animal and,under some circumstances,can be heard up to a distance of 8.9 km.Assume the acoustic output of a howler to be uniform in all directions and that the threshold of hearing is 1.0 × 10^-12 W/m².A juvenile howler monkey has an acoustic output of 63 µW.What is the ratio of the acoustic intensity produced by the juvenile howler to the reference intensity I₀,at a distance of 210 m?

A) 110
B) 230
C) 76
D) 170
E) 300

Question 18

When a rocket is traveling toward a mountain at 100 m/s,the sound waves from this rocket's engine approach the mountain at speed V.If the rocket doubles its speed to 200 m/s,the sound waves from the engine will now approach the mountain at speed

A) 4V.
B) 2V.
C) V.
D) V.

Question 19

An enclosed chamber with sound absorbing walls has a 2.0 m × 1.0 m opening for an outside window.A loudspeaker is located outdoors,78 m away and facing the window.The intensity level of the sound entering the window space from the loudspeaker is 79 dB.Assume the acoustic output of the loudspeaker is uniform in all directions and that the acoustic energy incident upon the ground is completely absorbed and therefore is not reflected into the window.The threshold of hearing is 1.0 × 10^-12 W/m².The acoustic power entering through the window space is closest to

A) 160 µW.
B) 79 µW.
C) 320 µW.
D) 790 µW.
E) 1600 µW.

Question 20

An enclosed chamber with sound absorbing walls has a 2.0 m × 1.0 m opening for an outside window.A loudspeaker is located outdoors,84 m away and facing the window.The intensity level of the sound entering the window space from the loudspeaker is 56 dB.Assume the acoustic output of the loudspeaker is uniform in all directions and that acoustic energy incident upon the ground is completely absorbed and therefore is not reflected into the window.The threshold of hearing is 1.0 × 10^-12 W/m².The acoustic power output of the loudspeaker is closest to

A) 0.035 W.
B) 0.070 W.
C) 0.18 W.
D) 0.35 W.
E) 0.70 W.

Question 21

A woman is riding a bicycle at 18.0 m/s along a straight road that runs parallel to and right next to some railroad tracks.She hears the whistle of a train that is behind.The frequency emitted by the train is 840 Hz,but the frequency the woman hears is 778 Hz.Take the speed of sound to be 340 m/s.
(a)What is the speed of the train,and is the train traveling away from or toward the bicycle?
(b)What frequency is heard by a stationary observer located between the train and the bicycle?

Question 22

A bat emits a sound at a frequency of 30.0 kHz as it approaches a wall.The bat detects beats such that the frequency of the echo is 900 Hz higher than the frequency the bat is emitting.The speed of sound in air is 340 m/s.The speed of the bat is closest to

A) 20.0 m/s.
B) 530 m/s.
C) 10.0 m/s.
D) 30.0 m/s.
E) 5.02 m/s.

Question 23

You are driving along a highway at 35.0 m/s when you hear the siren of a police car approaching you from behind and you perceive the frequency as 1370 Hz.You are relieved that he is in pursuit of a different speeder when he continues past you,but now you perceive the frequency as 1330 Hz.What is the speed of the police car? The speed of sound in air is 343 m/s.

A) 38.4 m/s
B) 30.0 m/s
C) 39.2 m/s
D) 40.0 m/s
E) 41.7 m/s

Question 24

A carousel that is 5.00 m in radius has a pair of 600-Hz sirens mounted on posts at opposite ends of a diameter.The carousel rotates with an angular velocity of 0.800 rad/s. A stationary listener is located at a distance from the carousel.The speed of sound is 350 m/s.The maximum beat frequency of the sirens at the position of the listener is closest to

A) 6 Hz.
B) 8 Hz.
C) 10 Hz.
D) 12 Hz.
E) 14 Hz.

Question 25

Two strings of identical material and radius are stretched with the same tension with their ends fixed,but one string is 8.0 mm longer than the other.Waves on these strings propagate at 420 m/s.The fundamental frequency of the longer string is 528 Hz.What is the beat frequency when each string is vibrating at its fundamental frequency?

A) 22 Hz
B) 11 Hz
C) 16 Hz
D) 5.5 Hz
E) 27 Hz

Question 26

If the intensity level at distance d of one trombone is 70 dB,what is the intensity level of 76 identical trombones,all at distance d?

A) 146 dB
B) 89 dB
C) 5320 dB
D) 76 dB
E) 82 dB

Question 27

The intensity level of a "Super-Silent" power lawn mower at a distance of 1.0 m is 100 dB.You wake up one morning to find that four of your neighbors are all mowing their lawns using identical "Super-Silent" mowers.When they are each 20 m from your open bedroom window,what is the intensity level of the sound in your bedroom? You can neglect any absorption,reflection,or interference of the sound.The lowest detectable intensity is 1.0 × 10^-12 W/m².

A) 80 dB
B) 104 dB
C) 400 dB
D) 50 dB
E) 40 dB

Question 28

A policeman in a stationary car measures the speed of approaching cars by means of an ultrasonic device that emits a sound with a frequency of 41.2 kHz.A car is approaching him at a speed of 33.0 m/s.The wave is reflected by the car and interferes with the emitted sound producing beats.What is the frequency of the beats? The speed of sound in air is 330 m/s.

A) 9.2 kHz
B) 4.1 kHz
C) 4.6 kHz
D) 1.2 kHz
E) 8.2 kHz

Question 29

A certain crying baby emits sound with an intensity of 8.0 × 10^-8 W/m².What is the intensity level due to a set of five such crying babies,all crying with the same intensity? You can neglect any absorption,reflection,or interference of the sound.The lowest detectable intensity is 1.0 × 10^-12 W/m².

A) 79 dB
B) 69 dB
C) 56 dB
D) 49 dB
E) 36 dB

Question 30

A person is hearing two sound waves simultaneously.One has a period of 1.50 ms and the other one a period of 1.54 ms.What is the period of the beat due to these two waves?

A) 0.040 ms
B) 1.5 ms
C) 3.0 ms
D) 58 ms
E) 330 ms

Question 31

At a distance of 2.00 m from a point source of sound,the intensity level is 80.0 dB.What will be the intensity level at a distance of 4.00 m from this source? The lowest detectable intensity is 1.0 × 10^-12 W/m².

A) 77.0 dB
B) 74.0 dB
C) 60.0 dB
D) 40.0 dB
E) 20.0 dB

Question 32

A carousel that is 5.00 m in radius has a pair of 600-Hz sirens mounted on posts at opposite ends of a diameter.The carousel rotates with an angular velocity of 0.800 rad/s. A stationary listener is located at a distance from the carousel.The speed of sound is 350 m/s.The longest wavelength reaching the listener from the sirens is closest to

A) 57.0 cm.
B) 57.7 cm.
C) 58.3 cm.
D) 59.0 cm.
E) 59.6 cm.

Question 33

The tension in each of two strings is adjusted so that both vibrate at exactly 666 Hz.The tension in one of the strings is then increased slightly.As a result,six beats per second are heard when both strings vibrate.What is the new frequency of the string that was tightened?

A) 672 Hz
B) 660 Hz
C) 669 Hz
D) 663 Hz

Question 34

Two motors in a factory are running at slightly different rates.One runs at 825 rpm and the other at 786 rpm.You hear the sound intensity increase and then decrease periodically due to wave interference.How much time elapses between successive maxima of the sound intensity?

A) 1.5 s
B) 1.4 s
C) 1.7 s
D) 1.8 s

Question 35

A boy on a bicycle approaches a brick wall as he sounds his horn at a frequency 400.00 Hz. The sound he hears reflected back from the wall is at a frequency 408.00 Hz. At what is the speed is the boy riding his bicycle toward the wall? Assume the speed of sound in air is 340 m/s.

A) 3.68 m/s
B) 333 m/s
C) 6.67 m/s
D) 6.80 m/s
E) 3.37 m/s

Question 36

As you stand by the side of the road,a car approaches you at a constant speed,sounding its horn,and you hear a frequency of 80.0 Hz.After the car goes by,you hear a frequency of 60.0 Hz.What is the speed of the car? The speed of sound in the air is 343 m/s.

A) 64.0 m/s
B) 49.0 m/s
C) 16.0 m/s
D) 36.0 m/s
E) 25.0 m/s

Question 37

Two harmonic sound waves reach an observer simultaneously. The observer hears the sound intensity rise and fall with a time of 0.200 s between the maximum intensity and the succeeding minimum intensity. What is the difference in frequency of the two sound waves?

A) 10.0 Hz
B) 0.200 Hz
C) 5.00 Hz
D) 2.50 Hz
E) 1.25 Hz

Question 38

A factory siren indicating the end of a shift has a frequency of 90.0 Hz.The speed of sound is 343 m/s.
(a)What frequency is perceived by the occupant of a car traveling towards the factory at 25.0 m/s?
(b)What frequency is perceived by the occupant of a car traveling away from the factory at 30.0 m/s?

Question 39

Two in-phase loudspeakers are some distance apart.They emit sound with a frequency of 1536 Hz.You move between the speakers,along the line joining them,at a constant speed of 2.8 m/s.What beat frequency do you observe? The speed of sound in the room is 330 m/s.

A) 13 Hz
B) 431 Hz
C) 26 Hz
D) 4.7 Hz
E) 118 Hz

Question 40

You are driving along a highway at 35.0 m/s when you hear the siren of a police car approaching you from behind and you perceive the frequency as 1310 Hz.You are relieved that he is in pursuit of a different speeder when he continues past you,but now you perceive the frequency as 1240 Hz.What is the frequency of the siren in the police car? The speed of sound in air is 343 m/s.

A) 1300 Hz
B) 1320 Hz
C) 1270 Hz
D) 1360 Hz
E) 1370 Hz

Question 41

A supersonic plane passes overhead at a speed of 500 m/s. If you hear the sonic boom (shock wave)4.00 s after the plane is directly overhead,at what altitude is the plane flying? Assume the speed of sound in air is 340 m/s.

A) 1.36 km
B) 2.16 km
C) 1.85 km
D) 2.45 km
E) The plane is not flying fast enough to produce a shock wave.

Question 42

An airplane flying faster than the speed of sound of 340 m/s produces a shock wave that makes an angle of 50° with the direction the plane is flying.What is the speed of the plane?

A) 490 m/s
B) 530 m/s
C) 390 m/s
D) 440 m/s
E) 405 m/s

Question 43

A jet aircraft,in level flight at constant speed,is observed directly overhead.A sonic boom is heard 13.0 s later,at which time the line of sight to the aircraft forms a 51° angle with respect to the horizontal.The speed of sound is 325 m/s.The altitude of the aircraft is closest to

A) 6700 m.
B) 5400 m.
C) 8300 m.
D) 2700 m.
E) 13,000 m.

Question 44

A jet aircraft,in level flight at constant speed,is observed directly overhead.A sonic boom is heard later,at which time the line of sight to the aircraft forms a 56° angle with respect to the horizontal.The speed of sound is 325 m/s.What is the Mach number (the ratio of the speed of the jet to the speed of sound)for the aircraft?

A) 1.2
B) 1.8
C) 1.9
D) 2.1
E) 2.2