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Essential University Physics, 3e (Wolfson) Chapter 14 Wave Motion 14.1 Conceptual Questions 1) Four traveling waves are described by the following equations, where all quantities are measured in SI units and y represents the displacement. I: y = 0.12 cos(3x - 21t) II: y = 0.15 sin(6x + 42t) III: y = 0.13 cos(6x + 21t) IV: y = -0.27 sin(3x - 42t) Which of these waves have the same period? A) I and III, and also II and IV B) I and IV, and also II and III C) I and II, and also III and IV D) All of them have the same period. E) They all have different periods. Answer: A Var: 1

2) Four traveling waves are described by the following equations, where all quantities are measured in SI units and y represents the displacement. I: y = 0.12 cos(3x + 2t) II: y = 0.15 sin(6x - 3t) III: y = 0.23 cos(3x + 6t) IV: y = -0.29 sin(1.5x - t) Which of these waves have the same speed? A) I and III B) I and IV C) II and III D) I and II E) III and IV Answer: B Var: 1

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3) For the wave shown in the figure, the wavelength is

A) 8 m. B) 4 m. C) 2 m. D) 1 m. E) unable to be determined from the given information. Answer: E Var: 1

4) For the wave shown in the figure, the frequency is

A) 0.5 Hz. B) 1 Hz. C) 2 Hz. D) 4 Hz. E) unable to be determined from the given information. Answer: A Var: 1

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5) The figure shows the displacement y of a traveling wave at a given position as a function of time and the displacement of the same wave at a given time as a function of position. Determine the wavelength of the wave.

A) 2.0 cm B) 3.0 m C) 2.0 m D) 4.0 m E) 1.5 m Answer: B Var: 1

6) The figure shows the displacement y of a wave at a given position as a function of time and the displacement of the same wave at a given time as a function of position. Determine the frequency of the wave.

A) 4.0 Hz B) 0.50 Hz C) 3.0 Hz D) 0.33 Hz E) 0.25 Hz Answer: E Var: 1

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7) When a weight W is hanging from a light vertical string, the speed of pulses on the string is V. If a second weight W is added without stretching the string, the speed of pulses on this string will now become A) 2V. B) V. C) V. D) V/ . E) V/2 Answer: B Var: 1

8) You are generating traveling waves on a stretched string by wiggling one end. If you suddenly begin to wiggle more rapidly without appreciably affecting the tension, you will cause the waves to move down the string A) faster than before. B) slower than before. C) at the same speed as before. Answer: C Var: 1

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9) In the figure, which of the curves best represents the variation of wave speed as a function of tension for transverse waves on a stretched string?

A) A B) B C) C D) D E) E Answer: B Var: 1

10) 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: D Var: 1

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11) A wave pulse traveling to the right along a thin cord reaches a discontinuity where the rope becomes thinner and lighter. What is the orientation of the reflected and transmitted pulses? A) Both pulses are right side up. B) The reflected pulse returns right side up while the transmitted pulse is inverted. C) The reflected pulse returns inverted while the transmitted pulse is right side up. D) Both pulses are inverted. Answer: A Var: 1

12) A wave pulse traveling to the right along a thin cord reaches a discontinuity where the rope becomes thicker and heavier. What is the orientation of the reflected and transmitted pulses? A) Both pulses are right side up. B) The reflected pulse returns right side up while the transmitted pulse is inverted. C) The reflected pulse returns inverted while the transmitted pulse is right side up. D) Both pulses are inverted. Answer: C Var: 1

13) A guitar string is fixed at both ends. If you tighten it to increase its tension A) the frequencies of its vibrational modes will increase but its wavelengths will not be affected. B) the wavelength increases but the frequency is not affected. C) both the frequency and the wavelength increase. Answer: A Var: 1

14) A tube open at one end and closed at the other end produces sound having a fundamental frequency of 350 Hz. If you now open the closed end, the fundamental frequency becomes A) 87.5 Hz. B) 175 Hz. C) 350 Hz. D) 700 Hz. E) 1400 Hz. Answer: B Var: 1

15) Consider the waves on a vibrating guitar string and the sound waves the guitar produces in the surrounding air. The string waves and the sound waves must have the same A) wavelength. B) velocity. C) frequency. D) amplitude. E) More than one of the above is true. Answer: C Var: 1

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16) What characteristic of sound determines the "pitch" of a musical note? A) amplitude B) wavelength C) frequency D) phase E) intensity Answer: C Var: 1

17) 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. Answer: D Var: 1

18) A pipe that is 120 cm long resonates to produce sound of wavelengths 480 cm, 160 cm, and 96 cm but does not resonate at any wavelengths longer than these. This pipe is A) open at both ends. B) open at one end and closed at the other end. C) closed at both ends. D) We cannot tell because we do not know the frequency of the sound. Answer: B Var: 1

19) Consider a pipe of length L that is open at both ends. What are the wavelengths of the three lowest-pitch tones produced by this pipe? A) 4L, 2L, L B) 2L, L, L/2 C) 2L, L, 2L/3 D) 4L, 4L/3, 4L/5 E) 2L, 2L, L/2 Answer: C Var: 1

20) The lowest-pitch tone to resonate in a pipe of length L that is open at both ends is 200 Hz. Which one of the following frequencies will NOT resonate in the same pipe? A) 400 Hz B) 600 Hz C) 800 Hz D) 900 Hz E) 1000 Hz Answer: D Var: 1

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21) In a resonating pipe that is open at both ends, there A) are displacement nodes at each end. B) are displacement antinodes at each end. C) is a displacement node at one end and a displacement antinode at the other end. D) None of the above are possible. Answer: B Var: 1

22) In a resonating pipe that is open at one end and closed at the other end, there A) are displacement nodes at each end. B) are displacement antinodes at each end. C) is a displacement node at the open end and a displacement antinode at the closed end. D) is a displacement node at the closed end and a displacement antinode at the open end. Answer: D Var: 1

23) The lowest-pitch tone to resonate in a pipe of length L that is closed at one end and open at the other end is 200 Hz. Which one of the following frequencies will NOT resonate in the same pipe? A) 400 Hz B) 600 Hz C) 1000 Hz D) 1400 Hz E) 1800 Hz Answer: A Var: 1

24) 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. Answer: E Var: 1

25) 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. Answer: D Var: 1

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26) 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. A) True B) False Answer: B Var: 1

27) 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: B Var: 1

28) 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. Answer: D Var: 1

14.2 Problems 1) The figure shows the displacement y of a traveling wave at a given position as a function of time and the displacement of the same wave at a given time as a function of position. How fast is the wave traveling?

A) 3.0 m/s B) 0.75 m/s C) 0.66 m/s D) 1.5 m/s E) 2.0 m/s Answer: B Var: 1 9 Copyright © 2016 Pearson Education, Inc.

2) Ocean tides are waves that have a period of 12 hours, an amplitude (in some places) of 1.50 m, and a speed of 750 km/hr. What is the distance between adjacent crests of these waves? A) 9000 km B) 32,400 km C) 9000 m D) 32,400 m E) 2500 m Answer: A Var: 1

3) The vertical displacement y(x,t) of a string stretched along the horizontal x-axis is given by y(x,t) = (6.00 mm) cos[(3.25 m-1)x - (7.22 rad/s)t]. (a) What is the minimum time for each complete cycle of the wave? (b) What is the distance between adjacent crests of the wave? (c) How fast does this wave travel? Answer: (a) 0.870 s (b) 1.93 m (c) 2.22 m/s Var: 1

4) A transverse wave is traveling on a string stretched along the horizontal x-axis. The equation for the vertical displacement y of the string is given by y = 0.0020 cos[π(15x - 52t)], where all quantities are in SI units. The maximum speed of a particle of the string is closest to A) 0.33 m/s. B) 0.43 m/s. C) 0.53 m/s. D) 0.64 m/s. E) 0.74 m/s. Answer: A Var: 1

5) Find the speed of an ocean wave whose vertical displacement y as a function of time t is given by y(x,t) = 3.7 cos(2.2x - 5.6t), where all quantities are in SI units. A) 2.5 m/s B) 1.9 m/s C) 3.5 m/s D) 4.5 m/s Answer: A Var: 1

6) You and your surfing buddy are waiting to catch a wave a few hundred meters off the beach. The waves are conveniently sinusoidal, and you notice that when you're on the top of one wave and moving toward your friend, she is exactly halfway between you and the trough of the wave. 1.50 seconds later, your friend is at the top of the wave. You estimate the horizontal distance between you and your friend at 8.00 m. (a) What is the frequency of the waves? (b) Find the speed of the waves. Answer: (a) 0.167 Hz (b) 5.33 m/s Var: 1

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7) Waves travel along a 100-m length of string which has a mass of 55 g and is held taut with a tension of 75 N. What is the speed of the waves? A) 3700 m/s B) 370 m/s C) 37 m/s D) 0.37 m/s E) 3.7 m/s Answer: B Var: 1

8) A 6.00-m long rope is under a tension of 600 N. Waves travel along this rope at 40.0 m/s. What is the mass of the rope? A) 1.00 kg B) 1.25 kg C) 2.25 kg D) 2.50 kg E) 1.12 kg Answer: C Var: 1

9) The density of aluminum is 2700 kg/m3. If transverse waves propagate at aluminum wire, what is the tension on the wire? A) 52 N B) 31 N C) 42 N D) 62 N Answer: A

in a

Var: 21

10) A 6.0-m wire with a mass of 50 g, is under tension. A transverse wave, for which the frequency is 810 Hz, the wavelength is 0.40 m, and the amplitude is 4.0 mm, is propagating on the wire. The time for a crest of this wave to travel the length of the wire is closest to A) 19 ms. B) 16 ms. C) 21 ms. D) 23 ms. E) 25 ms. Answer: A Var: 50+

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11) A 8.0-m long wire with a mass of 10 g is under tension. A transverse wave for which the frequency is 570 Hz, the wavelength is 0.10 m, and the amplitude is 3.7 mm is propagating on the wire. The maximum transverse acceleration of a point on a wire is closest to A) 47,000 m/s2. B) 41,000 m/s2. C) 35,000 m/s2. D) 29,000 m/s2. E) 53,000 m/s2. Answer: A Var: 50+

12) A heavy stone of mass m is hung from the ceiling by a thin 8.25-g wire that is 65.0 cm long. When you gently pluck the upper end of the wire, a pulse travels down the wire and returns 7.84 ms later, having reflected off the lower end. The stone is heavy enough to prevent the lower end of the wire from moving. What is the mass m of the stone? A) 8.90 kg B) 23.1 kg C) 35.6 kg D) 227 kg E) 349 kg Answer: C Var: 1

13) 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 Answer: A Var: 1

14) 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 Answer: A Var: 50+

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15) 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 Answer: A Var: 1

16) 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. Answer: C Var: 1

17) 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? Answer: (a) 12,900 W/m2 (at 2.50 m), 808 W/m2 (at 10.0 m) (b) 1.01 × 106 W Var: 1

18) A 2.00-m long piano wire with a mass per unit length of 12.0 g/m is under a tension of 8.00 kN. What is the frequency of the fundamental mode of vibration of this wire? A) 204 Hz B) 102 Hz C) 408 Hz D) 510 Hz E) 153 Hz Answer: A Var: 1

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19) A platinum wire that is 1.20 m long has a radius of 0.500 mm and is fixed at both ends. In its third harmonic it vibrates at 512 Hz. The density of platinum is 21.4 × 103 kg/m3. What is the tension in the wire? A) 4.00 kN B) 2.00 kN C) 2.82 kN D) 1.41 kN E) 1.00 kN Answer: C Var: 1

20) A thin taut string is fixed at both ends and stretched along the horizontal x-axis with its left end at x = 0. It is vibrating in its third OVERTONE, and the equation for the vertical displacement of any point on the string is y(x,t) = (1.22 cm) sin[(14.4 m-1)x] cos[(166 rad/s)t]. (a) What are the frequency and wavelength of the fundamental mode of this string? (b) How long is the string? (c) How fast do waves travel on this string? Answer: (a) 6.60 Hz, 1.75 m (b) 0.873 m (c) 11.5 m/s Var: 1

21) A thin 2.00-m string of mass 50.0 g is fixed at both ends and under a tension of 70.0 N. If it is set into small-amplitude oscillation, what is the frequency of the first harmonic mode? A) 6.61 Hz B) 13.2 Hz C) 26.5 Hz D) 52.9 Hz Answer: B Var: 1

22) A guitar string 0.650 m long has a tension of 61.0 N and a mass per unit length of 3.00 g/m. (a) What is the speed of waves on the string when it is plucked? (b) What is the string's fundamental frequency of vibration when plucked? Answer: (a) 143 m/s (b) 110 Hz Var: 1

23) A standing wave is oscillating at 690 Hz on a string, as shown in the figure. What is the speed of traveling waves on this string?

A) 280 m/s B) 410 m/s C) 210 m/s D) 140 m/s Answer: A Var: 50+ 14 Copyright © 2016 Pearson Education, Inc.

24) A 2.0-m string is fixed at both ends and tightened until the wave speed is frequency of the standing wave shown in the figure?

What is the

A) 120 Hz B) 230 Hz C) 350 Hz D) 470 Hz Answer: A Var: 50+

25) A 1.0-g string that is 0.64 m long is fixed at both ends and is under tension. This string produces a 100-Hz tone when it vibrates in the third harmonic. The speed of sound in air is 344 m/s. The tension in the string, in is closest to A) 2.8 N. B) 2.3 N. C) 1.8 N. D) 3.4 N. E) 3.9 N. Answer: A Var: 50+

26) A heavy stone of mass m is hung from the ceiling by a thin 8.25-g wire that is 65.0 cm long. When you gently pluck the upper end of the wire, a pulse travels down the wire and returns 7.84 ms later, having reflected off the lower end. The speed of sound in the room is 344 m/s, and the stone is heavy enough to prevent the lower end of the wire from moving. If the wire is vibrating in its second overtone, what is the frequency of the sound it will produce? A) 128 Hz B) 191 Hz C) 255 Hz D) 383 Hz E) 765 Hz Answer: D Var: 1

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27) A heavy stone of mass m is hung from the ceiling by a thin 8.25-g wire that is 65.0 cm long. When you gently pluck the upper end of the wire, a pulse travels down the wire and returns 7.84 ms later, having reflected off the lower end. The speed of sound in the room is 344 m/s, and the stone is heavy enough to prevent the lower end of the wire from moving. If the wire is vibrating in its second overtone, what is the wavelength of the sound it will produce? A) 0.217 m B) 0.433 m C) 0.650 m D) 0.899 m E) 1.35 m Answer: D Var: 1

28) Two violinists are trying to tune their instruments in an orchestra. One is producing the desired frequency of 440.0 Hz. The other is producing a frequency of 448.4 Hz. By what percentage should the out-of-tune musician change the tension in his string to bring his instrument into tune at 440.0 Hz? A) +1.9% B) -1.9% C) +3.7% D) -3.7% E) +8.4% Answer: D Var: 1

29) Standing waves of frequency 57 Hz are produced on a string that has mass per unit length 0.0160 kg/m. With what tension must the string be stretched between two supports if adjacent nodes in the standing wave are to be 0.71 meters apart? Answer: 100 N Var: 50+

30) 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.) Answer: 6.3 × 10-4 W Var: 50+

31) 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. Answer: A Var: 1 16 Copyright © 2016 Pearson Education, Inc.

32) 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 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 Answer: A Var: 50+

33) 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. Answer: A Var: 50+

34) 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. Answer: A Var: 50+

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35) 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 Answer: A Var: 5

36) 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: D Var: 1

37) 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 Answer: C Var: 1

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38) 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 Answer: A Var: 1

39) 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 Answer: B Var: 1

40) 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 Answer: B Var: 1

41) The speed of sound in the air inside a 0.640-m long gas column is 340 m/s. What is the fundamental resonant frequency of this air column if it is (a) open at one end and closed at the other end? (b) open at both ends? Answer: (a) 133 Hz (b) 266 Hz Var: 1

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42) A 1.30-m long gas column that is open at one end and closed at the other end has a fundamental resonant frequency 80.0 Hz. What is the speed of sound in this gas? A) 104 m/s B) 61.5 m/s C) 26.0 m/s D) 246 m/s E) 416 m/s Answer: E Var: 5

43) An air column, open at one end and closed at the other, is being designed so that its second lowest resonant frequency is 440 Hz. What should be the length of the column if the speed of sound in air is 340 m/s? A) 0.386 m B) 0.772 m C) 1.16 m D) 0.193 m E) 0.580 m Answer: E Var: 1

44) One of the harmonics of a column of air open at one end and closed at the other has a frequency of 448 Hz and the next higher harmonic has a frequency of 576 Hz. What is the fundamental frequency of the air column? A) 32 Hz B) 64 Hz C) 88 Hz D) 128 Hz E) 256 Hz Answer: B Var: 1

45) A violin with string length 32 cm and string density resonates with the first overtone from a 2.0-m long organ pipe with one end closed and the other end open. What is the tension in the string? A) 1000 N B) 110 N C) 450 N D) 4100 N E) 56 N Answer: A Var: 50+

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46) 50) A 0.25-m string, vibrating in its sixth harmonic, excites a 0.96-m pipe that is open at both ends into its second overtone resonance. The speed of sound in air is 345 m/s. The common resonant frequency of the string and the pipe is closest to A) 540 Hz. B) 360 Hz. C) 450 Hz. D) 630 Hz. E) 700 Hz. Answer: A Var: 1

47) A string, 0.28 m long and vibrating in its third harmonic, excites an open pipe that is 0.82 m long into its second overtone resonance. The speed of sound in air is 345 m/s. The speed of transverse waves on the string is closest to A) 120 m/s. B) 110 m/s. C) 100 m/s. D) 98 m/s. E) 91 m/s. Answer: A Var: 1

48) A pipe that is 0.46 m long and open at both ends vibrates in the second overtone with a frequency of In this situation, the distance from the center of the pipe to the nearest antinode is closest to A) 7.7 cm. B) 3.8 cm. C) 12 cm. D) 15 cm. E) zero. Answer: A Var: 50+

49) A pipe is 0.90 m long and is open at one end but closed at the other end. If it resonates with a tone whose wavelength is 0.72 m, what is the wavelength of the next higher overtone in this pipe? A) 0.36 m B) 0.40 m C) 0.45 m D) 0.51 m E) 0.58 m Answer: D Var: 1

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50) An organ pipe open at both ends has two successive harmonics with frequencies of 210 Hz and 240 Hz. What is the length of the pipe? The speed of sound is 344 m/s in air. A) 5.25 m B) 5.73 m C) 2.76 m D) 4.90 m E) 3.62 m Answer: B Var: 1

51) A string 40.0 cm long of mass 8.50 g is fixed at both ends and is under a tension of 425 N. When this string is vibrating in its third OVERTONE, you observe that it causes a nearby pipe, open at both ends, to resonate in its third HARMONIC. The speed of sound in the room is 344 m/s. (a) How long is the pipe? (b) What is the fundamental frequency of the pipe? Answer: (a) 0.730 m (b) 236 Hz Var: 1

52) The sound from a single source can reach point O by two different paths. One path is 20.0 m long and the second path is 21.0 m long. The sound destructively interferes at point O. What is the minimum frequency of the source if the speed of sound is 340 m/s? A) 340 Hz B) 6800 Hz C) 520 Hz D) 680 Hz E) 170 Hz Answer: E Var: 1

53) Two in-phase loudspeakers that emit sound with the same frequency are placed along a wall and are separated by a distance of 5.00 m. A person is standing 12.0 m away from the wall, equidistant from the loudspeakers. When the person moves 1.00 m parallel to the wall, she experiences destructive interference for the first time. What is the frequency of the sound? The speed of sound in air is 343 m/s. A) 211 Hz B) 256 Hz C) 422 Hz D) 512 Hz E) 674 Hz Answer: C Var: 1

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54) Two in-phase loudspeakers that emit sound with the same frequency are placed along a wall and are separated by a distance of 8.00 m. A person is standing 12.0 m away from the wall, equidistant from the loudspeakers. When the person moves 3.00 m parallel to the wall, she experiences destructive interference for the second time. What is the frequency of the sound? The speed of sound in the room is 343 m/s. CAREFUL! The distance to the wall is NOT much greater than the distance between the speakers. A) 278 Hz B) 422 Hz C) 452 Hz D) 562 Hz E) 694 Hz Answer: A Var: 1

55) Two stereo speakers mounted 4.52 m apart on a wall emit identical in-phase sound waves. You are standing at the opposite wall of the room at a point directly between the two speakers. You walk 2.11 m parallel to the wall, to a location where you first notice that the sound intensity drops to zero. If the wall along which you are walking is 10.7 m from the wall with the speakers, what is the wavelength of the sound waves? CAREFUL! The distance to the wall is NOT much greater than the distance between the speakers. A) 1.7 m B) 2.1 m C) 2.6 m D) 2.9 m Answer: A Var: 1

56) Radio station KBOB broadcasts at a frequency of 85.7 MHz on your dial using radio waves that travel at 3.00 × 108 m/s. Since most of the station's audience is due south of the transmitter, the managers of KBOB don't want to waste any energy broadcasting to the east and west. They decide to build two towers, transmitting in phase at exactly the same frequency, aligned on an east-west axis. For engineering reasons, the two towers must be AT LEAST 10.0 m apart. What is the shortest distance between the towers that will eliminate all broadcast power to the east and west? Answer: 12.3 m Var: 1

57) Two loudspeakers placed 6.0 m apart are driven in phase by an audio oscillator whose frequency range is to A point P is located from one loudspeaker and 3.6 m from the other. The speed of sound is 344 m/s. The frequency produced by the oscillator, for which constructive interference of sound occurs at point P, is closest to A) 2580 Hz. B) 2903 Hz. C) 2473 Hz. D) 2795 Hz. E) 2688 Hz. Answer: A Var: 50+ 23 Copyright © 2016 Pearson Education, Inc.

58) Two identical loudspeakers that are 5.00 m apart and face toward each other are driven in phase by the same oscillator at a frequency of 875 Hz. The speed of sound in the room is 344 m/s. If you start out standing midway between the speakers, find the shortest distance you can walk toward either speaker in order to hear a minimum of sound. A) 0.0983 m B) 0.197 m C) 0.295 m D) 0.393 m E) 0.590 m Answer: A Var: 1

59) 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 Answer: D Var: 1

60) 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 Answer: D Var: 1

61) 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 Answer: A Var: 1

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62) 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 Answer: A Var: 50+

63) 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 Answer: B Var: 1

64) 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? Answer: (a) 7.67 m/s, away from the bicycle (b) 821 Hz Var: 1

65) 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? Answer: (a) 96.6 Hz (b) 82.1 Hz Var: 1

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66) 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 Answer: B Var: 1

67) 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 Answer: E Var: 1

68) 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 Answer: D Var: 5

69) 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 Answer: C Var: 5

70) 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 26 Copyright © 2016 Pearson Education, Inc.

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. Answer: E Var: 1

71) 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 Answer: C Var: 1

72) 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 Answer: A Var: 1

73) 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. Answer: D Var: 1

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74) 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. Answer: E Var: 1

75) 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 Answer: D Var: 1

76) 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. Answer: C Var: 1

77) 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 Answer: A Var: 50+

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78) A jet aircraft, in level flight at constant speed, is observed directly over head. A sonic boom is heard 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. Answer: A Var: 50+

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2) Four traveling waves are described by the following equations, where all quantities are measured in SI units and y represents the displacement. I: y = 0.12 cos(3x + 2t) II: y = 0.15 sin(6x - 3t) III: y = 0.23 cos(3x + 6t) IV: y = -0.29 sin(1.5x - t) Which of these waves have the same speed? A) I and III B) I and IV C) II and III D) I and II E) III and IV Answer: B Var: 1

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3) For the wave shown in the figure, the wavelength is

A) 8 m. B) 4 m. C) 2 m. D) 1 m. E) unable to be determined from the given information. Answer: E Var: 1

4) For the wave shown in the figure, the frequency is

A) 0.5 Hz. B) 1 Hz. C) 2 Hz. D) 4 Hz. E) unable to be determined from the given information. Answer: A Var: 1

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5) The figure shows the displacement y of a traveling wave at a given position as a function of time and the displacement of the same wave at a given time as a function of position. Determine the wavelength of the wave.

A) 2.0 cm B) 3.0 m C) 2.0 m D) 4.0 m E) 1.5 m Answer: B Var: 1

6) The figure shows the displacement y of a wave at a given position as a function of time and the displacement of the same wave at a given time as a function of position. Determine the frequency of the wave.

A) 4.0 Hz B) 0.50 Hz C) 3.0 Hz D) 0.33 Hz E) 0.25 Hz Answer: E Var: 1

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7) When a weight W is hanging from a light vertical string, the speed of pulses on the string is V. If a second weight W is added without stretching the string, the speed of pulses on this string will now become A) 2V. B) V. C) V. D) V/ . E) V/2 Answer: B Var: 1

8) You are generating traveling waves on a stretched string by wiggling one end. If you suddenly begin to wiggle more rapidly without appreciably affecting the tension, you will cause the waves to move down the string A) faster than before. B) slower than before. C) at the same speed as before. Answer: C Var: 1

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9) In the figure, which of the curves best represents the variation of wave speed as a function of tension for transverse waves on a stretched string?

A) A B) B C) C D) D E) E Answer: B Var: 1

10) 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: D Var: 1

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11) A wave pulse traveling to the right along a thin cord reaches a discontinuity where the rope becomes thinner and lighter. What is the orientation of the reflected and transmitted pulses? A) Both pulses are right side up. B) The reflected pulse returns right side up while the transmitted pulse is inverted. C) The reflected pulse returns inverted while the transmitted pulse is right side up. D) Both pulses are inverted. Answer: A Var: 1

12) A wave pulse traveling to the right along a thin cord reaches a discontinuity where the rope becomes thicker and heavier. What is the orientation of the reflected and transmitted pulses? A) Both pulses are right side up. B) The reflected pulse returns right side up while the transmitted pulse is inverted. C) The reflected pulse returns inverted while the transmitted pulse is right side up. D) Both pulses are inverted. Answer: C Var: 1

13) A guitar string is fixed at both ends. If you tighten it to increase its tension A) the frequencies of its vibrational modes will increase but its wavelengths will not be affected. B) the wavelength increases but the frequency is not affected. C) both the frequency and the wavelength increase. Answer: A Var: 1

14) A tube open at one end and closed at the other end produces sound having a fundamental frequency of 350 Hz. If you now open the closed end, the fundamental frequency becomes A) 87.5 Hz. B) 175 Hz. C) 350 Hz. D) 700 Hz. E) 1400 Hz. Answer: B Var: 1

15) Consider the waves on a vibrating guitar string and the sound waves the guitar produces in the surrounding air. The string waves and the sound waves must have the same A) wavelength. B) velocity. C) frequency. D) amplitude. E) More than one of the above is true. Answer: C Var: 1

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16) What characteristic of sound determines the "pitch" of a musical note? A) amplitude B) wavelength C) frequency D) phase E) intensity Answer: C Var: 1

17) 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. Answer: D Var: 1

18) A pipe that is 120 cm long resonates to produce sound of wavelengths 480 cm, 160 cm, and 96 cm but does not resonate at any wavelengths longer than these. This pipe is A) open at both ends. B) open at one end and closed at the other end. C) closed at both ends. D) We cannot tell because we do not know the frequency of the sound. Answer: B Var: 1

19) Consider a pipe of length L that is open at both ends. What are the wavelengths of the three lowest-pitch tones produced by this pipe? A) 4L, 2L, L B) 2L, L, L/2 C) 2L, L, 2L/3 D) 4L, 4L/3, 4L/5 E) 2L, 2L, L/2 Answer: C Var: 1

20) The lowest-pitch tone to resonate in a pipe of length L that is open at both ends is 200 Hz. Which one of the following frequencies will NOT resonate in the same pipe? A) 400 Hz B) 600 Hz C) 800 Hz D) 900 Hz E) 1000 Hz Answer: D Var: 1

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21) In a resonating pipe that is open at both ends, there A) are displacement nodes at each end. B) are displacement antinodes at each end. C) is a displacement node at one end and a displacement antinode at the other end. D) None of the above are possible. Answer: B Var: 1

22) In a resonating pipe that is open at one end and closed at the other end, there A) are displacement nodes at each end. B) are displacement antinodes at each end. C) is a displacement node at the open end and a displacement antinode at the closed end. D) is a displacement node at the closed end and a displacement antinode at the open end. Answer: D Var: 1

23) The lowest-pitch tone to resonate in a pipe of length L that is closed at one end and open at the other end is 200 Hz. Which one of the following frequencies will NOT resonate in the same pipe? A) 400 Hz B) 600 Hz C) 1000 Hz D) 1400 Hz E) 1800 Hz Answer: A Var: 1

24) 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. Answer: E Var: 1

25) 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. Answer: D Var: 1

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26) 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. A) True B) False Answer: B Var: 1

27) 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: B Var: 1

28) 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. Answer: D Var: 1

14.2 Problems 1) The figure shows the displacement y of a traveling wave at a given position as a function of time and the displacement of the same wave at a given time as a function of position. How fast is the wave traveling?

A) 3.0 m/s B) 0.75 m/s C) 0.66 m/s D) 1.5 m/s E) 2.0 m/s Answer: B Var: 1 9 Copyright © 2016 Pearson Education, Inc.

2) Ocean tides are waves that have a period of 12 hours, an amplitude (in some places) of 1.50 m, and a speed of 750 km/hr. What is the distance between adjacent crests of these waves? A) 9000 km B) 32,400 km C) 9000 m D) 32,400 m E) 2500 m Answer: A Var: 1

3) The vertical displacement y(x,t) of a string stretched along the horizontal x-axis is given by y(x,t) = (6.00 mm) cos[(3.25 m-1)x - (7.22 rad/s)t]. (a) What is the minimum time for each complete cycle of the wave? (b) What is the distance between adjacent crests of the wave? (c) How fast does this wave travel? Answer: (a) 0.870 s (b) 1.93 m (c) 2.22 m/s Var: 1

4) A transverse wave is traveling on a string stretched along the horizontal x-axis. The equation for the vertical displacement y of the string is given by y = 0.0020 cos[π(15x - 52t)], where all quantities are in SI units. The maximum speed of a particle of the string is closest to A) 0.33 m/s. B) 0.43 m/s. C) 0.53 m/s. D) 0.64 m/s. E) 0.74 m/s. Answer: A Var: 1

5) Find the speed of an ocean wave whose vertical displacement y as a function of time t is given by y(x,t) = 3.7 cos(2.2x - 5.6t), where all quantities are in SI units. A) 2.5 m/s B) 1.9 m/s C) 3.5 m/s D) 4.5 m/s Answer: A Var: 1

6) You and your surfing buddy are waiting to catch a wave a few hundred meters off the beach. The waves are conveniently sinusoidal, and you notice that when you're on the top of one wave and moving toward your friend, she is exactly halfway between you and the trough of the wave. 1.50 seconds later, your friend is at the top of the wave. You estimate the horizontal distance between you and your friend at 8.00 m. (a) What is the frequency of the waves? (b) Find the speed of the waves. Answer: (a) 0.167 Hz (b) 5.33 m/s Var: 1

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7) Waves travel along a 100-m length of string which has a mass of 55 g and is held taut with a tension of 75 N. What is the speed of the waves? A) 3700 m/s B) 370 m/s C) 37 m/s D) 0.37 m/s E) 3.7 m/s Answer: B Var: 1

8) A 6.00-m long rope is under a tension of 600 N. Waves travel along this rope at 40.0 m/s. What is the mass of the rope? A) 1.00 kg B) 1.25 kg C) 2.25 kg D) 2.50 kg E) 1.12 kg Answer: C Var: 1

9) The density of aluminum is 2700 kg/m3. If transverse waves propagate at aluminum wire, what is the tension on the wire? A) 52 N B) 31 N C) 42 N D) 62 N Answer: A

in a

Var: 21

10) A 6.0-m wire with a mass of 50 g, is under tension. A transverse wave, for which the frequency is 810 Hz, the wavelength is 0.40 m, and the amplitude is 4.0 mm, is propagating on the wire. The time for a crest of this wave to travel the length of the wire is closest to A) 19 ms. B) 16 ms. C) 21 ms. D) 23 ms. E) 25 ms. Answer: A Var: 50+

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11) A 8.0-m long wire with a mass of 10 g is under tension. A transverse wave for which the frequency is 570 Hz, the wavelength is 0.10 m, and the amplitude is 3.7 mm is propagating on the wire. The maximum transverse acceleration of a point on a wire is closest to A) 47,000 m/s2. B) 41,000 m/s2. C) 35,000 m/s2. D) 29,000 m/s2. E) 53,000 m/s2. Answer: A Var: 50+

12) A heavy stone of mass m is hung from the ceiling by a thin 8.25-g wire that is 65.0 cm long. When you gently pluck the upper end of the wire, a pulse travels down the wire and returns 7.84 ms later, having reflected off the lower end. The stone is heavy enough to prevent the lower end of the wire from moving. What is the mass m of the stone? A) 8.90 kg B) 23.1 kg C) 35.6 kg D) 227 kg E) 349 kg Answer: C Var: 1

13) 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 Answer: A Var: 1

14) 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 Answer: A Var: 50+

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15) 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 Answer: A Var: 1

16) 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. Answer: C Var: 1

17) 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? Answer: (a) 12,900 W/m2 (at 2.50 m), 808 W/m2 (at 10.0 m) (b) 1.01 × 106 W Var: 1

18) A 2.00-m long piano wire with a mass per unit length of 12.0 g/m is under a tension of 8.00 kN. What is the frequency of the fundamental mode of vibration of this wire? A) 204 Hz B) 102 Hz C) 408 Hz D) 510 Hz E) 153 Hz Answer: A Var: 1

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19) A platinum wire that is 1.20 m long has a radius of 0.500 mm and is fixed at both ends. In its third harmonic it vibrates at 512 Hz. The density of platinum is 21.4 × 103 kg/m3. What is the tension in the wire? A) 4.00 kN B) 2.00 kN C) 2.82 kN D) 1.41 kN E) 1.00 kN Answer: C Var: 1

20) A thin taut string is fixed at both ends and stretched along the horizontal x-axis with its left end at x = 0. It is vibrating in its third OVERTONE, and the equation for the vertical displacement of any point on the string is y(x,t) = (1.22 cm) sin[(14.4 m-1)x] cos[(166 rad/s)t]. (a) What are the frequency and wavelength of the fundamental mode of this string? (b) How long is the string? (c) How fast do waves travel on this string? Answer: (a) 6.60 Hz, 1.75 m (b) 0.873 m (c) 11.5 m/s Var: 1

21) A thin 2.00-m string of mass 50.0 g is fixed at both ends and under a tension of 70.0 N. If it is set into small-amplitude oscillation, what is the frequency of the first harmonic mode? A) 6.61 Hz B) 13.2 Hz C) 26.5 Hz D) 52.9 Hz Answer: B Var: 1

22) A guitar string 0.650 m long has a tension of 61.0 N and a mass per unit length of 3.00 g/m. (a) What is the speed of waves on the string when it is plucked? (b) What is the string's fundamental frequency of vibration when plucked? Answer: (a) 143 m/s (b) 110 Hz Var: 1

23) A standing wave is oscillating at 690 Hz on a string, as shown in the figure. What is the speed of traveling waves on this string?

A) 280 m/s B) 410 m/s C) 210 m/s D) 140 m/s Answer: A Var: 50+ 14 Copyright © 2016 Pearson Education, Inc.

24) A 2.0-m string is fixed at both ends and tightened until the wave speed is frequency of the standing wave shown in the figure?

What is the

A) 120 Hz B) 230 Hz C) 350 Hz D) 470 Hz Answer: A Var: 50+

25) A 1.0-g string that is 0.64 m long is fixed at both ends and is under tension. This string produces a 100-Hz tone when it vibrates in the third harmonic. The speed of sound in air is 344 m/s. The tension in the string, in is closest to A) 2.8 N. B) 2.3 N. C) 1.8 N. D) 3.4 N. E) 3.9 N. Answer: A Var: 50+

26) A heavy stone of mass m is hung from the ceiling by a thin 8.25-g wire that is 65.0 cm long. When you gently pluck the upper end of the wire, a pulse travels down the wire and returns 7.84 ms later, having reflected off the lower end. The speed of sound in the room is 344 m/s, and the stone is heavy enough to prevent the lower end of the wire from moving. If the wire is vibrating in its second overtone, what is the frequency of the sound it will produce? A) 128 Hz B) 191 Hz C) 255 Hz D) 383 Hz E) 765 Hz Answer: D Var: 1

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27) A heavy stone of mass m is hung from the ceiling by a thin 8.25-g wire that is 65.0 cm long. When you gently pluck the upper end of the wire, a pulse travels down the wire and returns 7.84 ms later, having reflected off the lower end. The speed of sound in the room is 344 m/s, and the stone is heavy enough to prevent the lower end of the wire from moving. If the wire is vibrating in its second overtone, what is the wavelength of the sound it will produce? A) 0.217 m B) 0.433 m C) 0.650 m D) 0.899 m E) 1.35 m Answer: D Var: 1

28) Two violinists are trying to tune their instruments in an orchestra. One is producing the desired frequency of 440.0 Hz. The other is producing a frequency of 448.4 Hz. By what percentage should the out-of-tune musician change the tension in his string to bring his instrument into tune at 440.0 Hz? A) +1.9% B) -1.9% C) +3.7% D) -3.7% E) +8.4% Answer: D Var: 1

29) Standing waves of frequency 57 Hz are produced on a string that has mass per unit length 0.0160 kg/m. With what tension must the string be stretched between two supports if adjacent nodes in the standing wave are to be 0.71 meters apart? Answer: 100 N Var: 50+

30) 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.) Answer: 6.3 × 10-4 W Var: 50+

31) 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. Answer: A Var: 1 16 Copyright © 2016 Pearson Education, Inc.

32) 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 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 Answer: A Var: 50+

33) 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. Answer: A Var: 50+

34) 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. Answer: A Var: 50+

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35) 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 Answer: A Var: 5

36) 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: D Var: 1

37) 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 Answer: C Var: 1

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38) 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 Answer: A Var: 1

39) 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 Answer: B Var: 1

40) 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 Answer: B Var: 1

41) The speed of sound in the air inside a 0.640-m long gas column is 340 m/s. What is the fundamental resonant frequency of this air column if it is (a) open at one end and closed at the other end? (b) open at both ends? Answer: (a) 133 Hz (b) 266 Hz Var: 1

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42) A 1.30-m long gas column that is open at one end and closed at the other end has a fundamental resonant frequency 80.0 Hz. What is the speed of sound in this gas? A) 104 m/s B) 61.5 m/s C) 26.0 m/s D) 246 m/s E) 416 m/s Answer: E Var: 5

43) An air column, open at one end and closed at the other, is being designed so that its second lowest resonant frequency is 440 Hz. What should be the length of the column if the speed of sound in air is 340 m/s? A) 0.386 m B) 0.772 m C) 1.16 m D) 0.193 m E) 0.580 m Answer: E Var: 1

44) One of the harmonics of a column of air open at one end and closed at the other has a frequency of 448 Hz and the next higher harmonic has a frequency of 576 Hz. What is the fundamental frequency of the air column? A) 32 Hz B) 64 Hz C) 88 Hz D) 128 Hz E) 256 Hz Answer: B Var: 1

45) A violin with string length 32 cm and string density resonates with the first overtone from a 2.0-m long organ pipe with one end closed and the other end open. What is the tension in the string? A) 1000 N B) 110 N C) 450 N D) 4100 N E) 56 N Answer: A Var: 50+

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46) 50) A 0.25-m string, vibrating in its sixth harmonic, excites a 0.96-m pipe that is open at both ends into its second overtone resonance. The speed of sound in air is 345 m/s. The common resonant frequency of the string and the pipe is closest to A) 540 Hz. B) 360 Hz. C) 450 Hz. D) 630 Hz. E) 700 Hz. Answer: A Var: 1

47) A string, 0.28 m long and vibrating in its third harmonic, excites an open pipe that is 0.82 m long into its second overtone resonance. The speed of sound in air is 345 m/s. The speed of transverse waves on the string is closest to A) 120 m/s. B) 110 m/s. C) 100 m/s. D) 98 m/s. E) 91 m/s. Answer: A Var: 1

48) A pipe that is 0.46 m long and open at both ends vibrates in the second overtone with a frequency of In this situation, the distance from the center of the pipe to the nearest antinode is closest to A) 7.7 cm. B) 3.8 cm. C) 12 cm. D) 15 cm. E) zero. Answer: A Var: 50+

49) A pipe is 0.90 m long and is open at one end but closed at the other end. If it resonates with a tone whose wavelength is 0.72 m, what is the wavelength of the next higher overtone in this pipe? A) 0.36 m B) 0.40 m C) 0.45 m D) 0.51 m E) 0.58 m Answer: D Var: 1

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50) An organ pipe open at both ends has two successive harmonics with frequencies of 210 Hz and 240 Hz. What is the length of the pipe? The speed of sound is 344 m/s in air. A) 5.25 m B) 5.73 m C) 2.76 m D) 4.90 m E) 3.62 m Answer: B Var: 1

51) A string 40.0 cm long of mass 8.50 g is fixed at both ends and is under a tension of 425 N. When this string is vibrating in its third OVERTONE, you observe that it causes a nearby pipe, open at both ends, to resonate in its third HARMONIC. The speed of sound in the room is 344 m/s. (a) How long is the pipe? (b) What is the fundamental frequency of the pipe? Answer: (a) 0.730 m (b) 236 Hz Var: 1

52) The sound from a single source can reach point O by two different paths. One path is 20.0 m long and the second path is 21.0 m long. The sound destructively interferes at point O. What is the minimum frequency of the source if the speed of sound is 340 m/s? A) 340 Hz B) 6800 Hz C) 520 Hz D) 680 Hz E) 170 Hz Answer: E Var: 1

53) Two in-phase loudspeakers that emit sound with the same frequency are placed along a wall and are separated by a distance of 5.00 m. A person is standing 12.0 m away from the wall, equidistant from the loudspeakers. When the person moves 1.00 m parallel to the wall, she experiences destructive interference for the first time. What is the frequency of the sound? The speed of sound in air is 343 m/s. A) 211 Hz B) 256 Hz C) 422 Hz D) 512 Hz E) 674 Hz Answer: C Var: 1

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54) Two in-phase loudspeakers that emit sound with the same frequency are placed along a wall and are separated by a distance of 8.00 m. A person is standing 12.0 m away from the wall, equidistant from the loudspeakers. When the person moves 3.00 m parallel to the wall, she experiences destructive interference for the second time. What is the frequency of the sound? The speed of sound in the room is 343 m/s. CAREFUL! The distance to the wall is NOT much greater than the distance between the speakers. A) 278 Hz B) 422 Hz C) 452 Hz D) 562 Hz E) 694 Hz Answer: A Var: 1

55) Two stereo speakers mounted 4.52 m apart on a wall emit identical in-phase sound waves. You are standing at the opposite wall of the room at a point directly between the two speakers. You walk 2.11 m parallel to the wall, to a location where you first notice that the sound intensity drops to zero. If the wall along which you are walking is 10.7 m from the wall with the speakers, what is the wavelength of the sound waves? CAREFUL! The distance to the wall is NOT much greater than the distance between the speakers. A) 1.7 m B) 2.1 m C) 2.6 m D) 2.9 m Answer: A Var: 1

56) Radio station KBOB broadcasts at a frequency of 85.7 MHz on your dial using radio waves that travel at 3.00 × 108 m/s. Since most of the station's audience is due south of the transmitter, the managers of KBOB don't want to waste any energy broadcasting to the east and west. They decide to build two towers, transmitting in phase at exactly the same frequency, aligned on an east-west axis. For engineering reasons, the two towers must be AT LEAST 10.0 m apart. What is the shortest distance between the towers that will eliminate all broadcast power to the east and west? Answer: 12.3 m Var: 1

57) Two loudspeakers placed 6.0 m apart are driven in phase by an audio oscillator whose frequency range is to A point P is located from one loudspeaker and 3.6 m from the other. The speed of sound is 344 m/s. The frequency produced by the oscillator, for which constructive interference of sound occurs at point P, is closest to A) 2580 Hz. B) 2903 Hz. C) 2473 Hz. D) 2795 Hz. E) 2688 Hz. Answer: A Var: 50+ 23 Copyright © 2016 Pearson Education, Inc.

58) Two identical loudspeakers that are 5.00 m apart and face toward each other are driven in phase by the same oscillator at a frequency of 875 Hz. The speed of sound in the room is 344 m/s. If you start out standing midway between the speakers, find the shortest distance you can walk toward either speaker in order to hear a minimum of sound. A) 0.0983 m B) 0.197 m C) 0.295 m D) 0.393 m E) 0.590 m Answer: A Var: 1

59) 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 Answer: D Var: 1

60) 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 Answer: D Var: 1

61) 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 Answer: A Var: 1

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62) 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 Answer: A Var: 50+

63) 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 Answer: B Var: 1

64) 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? Answer: (a) 7.67 m/s, away from the bicycle (b) 821 Hz Var: 1

65) 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? Answer: (a) 96.6 Hz (b) 82.1 Hz Var: 1

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66) 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 Answer: B Var: 1

67) 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 Answer: E Var: 1

68) 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 Answer: D Var: 5

69) 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 Answer: C Var: 5

70) 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 26 Copyright © 2016 Pearson Education, Inc.

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. Answer: E Var: 1

71) 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 Answer: C Var: 1

72) 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 Answer: A Var: 1

73) 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. Answer: D Var: 1

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74) 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. Answer: E Var: 1

75) 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 Answer: D Var: 1

76) 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. Answer: C Var: 1

77) 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 Answer: A Var: 50+

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78) A jet aircraft, in level flight at constant speed, is observed directly over head. A sonic boom is heard 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. Answer: A Var: 50+

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