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A string fixed at both ends is vibrating in a standing wave. There are three nodes between the ends of the string, not including those on the ends. The string is vibrating at a frequency that is its


A) fundamental.
B) second harmonic.
C) third harmonic.
D) fourth harmonic.
E) fifth harmonic.

F) C) and E)
G) B) and E)

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A microphone is placed at the node of a standing sound wave. What does the microphone pick up?


A) A constant and very high intensity sound.
B) A constant and very low intensity sound.
C) A varying high intensity sound.
D) A varying low intensity sound.
E) Unable to tell.

F) A) and E)
G) All of the above

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Two speakers face each other at a distance of 1 m and are driven by a common audio oscillator. A first minimum in sound intensity is found 16.1 cm from the midpoint. If the velocity of sound is 330 m/s, find the frequency of the oscillator.


A) 256 Hz
B) 1024 Hz
C) 512 Hz
D) 341 Hz
E) 683 Hz

F) None of the above
G) C) and D)

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Waves of amplitude 1.1 cm and wavelength 40 cm move along a 12-m-long string that has a mass of 70 g and is under a tension of 15 N. Calculate the velocity of the wave.


A) 51 m/s
B) 2570 m/s
C) 16 m/s
D) 15 m/s
E) 331 m/s

F) A) and B)
G) A) and E)

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Two sounds differ by 20 dB. This means that the louder sound is _____ times as intense and _____ times as loud.


A) 20; 20
B) 100; 20
C) 20; 4
D) 100; 4
E) 2; 2

F) A) and D)
G) C) and D)

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  The figure shows a wave on a string approaching its fixed end at a wall. When the wave reaches the wall and is reflected, a standing wave will be set up in the string. One of the antinodes in the standing wave will be found at position A)  1. B)  2. C)  3. D)  4. E)  5. The figure shows a wave on a string approaching its fixed end at a wall. When the wave reaches the wall and is reflected, a standing wave will be set up in the string. One of the antinodes in the standing wave will be found at position


A) 1.
B) 2.
C) 3.
D) 4.
E) 5.

F) B) and C)
G) C) and E)

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  The figure shows several modes of vibration of a string fixed at both ends. The mode of vibration that represents the fifth harmonic is A)  1. B)  2. C)  3. D)  4. E)  None of these is correct. The figure shows several modes of vibration of a string fixed at both ends. The mode of vibration that represents the fifth harmonic is


A) 1.
B) 2.
C) 3.
D) 4.
E) None of these is correct.

F) A) and D)
G) A) and B)

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When the frequency of a source is doubled, the sound produced


A) travels at half its former speed.
B) travels at twice its former speed.
C) has half its former wavelength.
D) has twice its former wavelength.
E) is greatly improved in quality.

F) C) and D)
G) C) and E)

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A piano tuner hears a beat every 0.33 seconds when he hits a note and compares it to his reference tone at 163 Hz. What is the lowest possible frequency of the piano note?


A) 44.9 Hz
B) 166.0 Hz
C) 162.7 Hz
D) 163.3 Hz
E) 160.0 Hz

F) C) and E)
G) A) and C)

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If both the tension and the length of a vibrating string are doubled while the linear density remains constant, the fundamental frequency of the string is multiplied by


A) 1.
B) 2.
C) If both the tension and the length of a vibrating string are doubled while the linear density remains constant, the fundamental frequency of the string is multiplied by A)  1. B)  2. C)    D)    E)
D) If both the tension and the length of a vibrating string are doubled while the linear density remains constant, the fundamental frequency of the string is multiplied by A)  1. B)  2. C)    D)    E)
E) If both the tension and the length of a vibrating string are doubled while the linear density remains constant, the fundamental frequency of the string is multiplied by A)  1. B)  2. C)    D)    E)

F) A) and E)
G) C) and D)

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Geologists use explosives to map the subterranean. The times for the reflected waves to arrive at a monitoring station can tell a great deal about the composition of the rock structures. Suppose the time it takes for a wave that is reflected from the interface of 1) and 2) is 2 s, and the time for another wave that is reflected between 2) and 3) is 2.5 s, and the speed of the wave in layer 1) is 6 km/s and in layer 2) is 4 km/s, then how thick is layer 2) ? Geologists use explosives to map the subterranean. The times for the reflected waves to arrive at a monitoring station can tell a great deal about the composition of the rock structures. Suppose the time it takes for a wave that is reflected from the interface of 1)  and 2)  is 2 s, and the time for another wave that is reflected between 2)  and 3)  is 2.5 s, and the speed of the wave in layer 1)  is 6 km/s and in layer 2)  is 4 km/s, then how thick is layer 2) ?   A)  2 km B)  1 km C)  3 km D)  6 km E)  8 km


A) 2 km
B) 1 km
C) 3 km
D) 6 km
E) 8 km

F) B) and D)
G) A) and B)

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The standing waves in air in a pipe of length L that is open at both ends have a speed v. The frequencies of the three lowest harmonics are


A) "v/L, 2v/L, and 3v/L."
B) "v/2L, v/L, and 3v/2L."
C) " λ\lambda /2, λ\lambda , and 3 λ\lambda /2."
D) "L/v, 2L/v, and 3L/v."
E) " λ\lambda /3, 2 λ\lambda /3, and 3 λ\lambda /3."

F) A) and B)
G) B) and E)

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  Which curve best represents the variation of wave velocity with tension in a vibrating string? A)  1 B)  2 C)  3 D)  4 E)  5 Which curve best represents the variation of wave velocity with tension in a vibrating string?


A) 1
B) 2
C) 3
D) 4
E) 5

F) B) and E)
G) B) and D)

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The standing waves on a string of length L that is fixed at both ends have a speed v. The three lowest frequencies of vibration are


A) "v/L, 2v/L, and 3v/L."
B) "v/2L, v/L, and 3v/2L."
C) " λ\lambda /2, λ\lambda , and 3 λ\lambda /2."
D) "L/v, 2L/v, and 3L/v."
E) " λ\lambda /3, 2 λ\lambda /3, and 3 λ\lambda /3."

F) None of the above
G) A) and D)

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  A standing wave is created by oscillating a taut string at a frequency that corresponds to one of the resonant frequencies. The amplitude of the antinodes is very much larger than the amplitude of the oscillator. Does this violate the conservation of energy principle? Explain why. A)  Yes, since E is proportional to amplitude squared. B)  Yes, since there is large kinetic energy of the string, and this is much bigger than the energy from the oscillator. C)  No, energy from waves does not obey the conservation of energy principle in the first place. D)  No, the energy at the antinodes builds up after the first few cycles, after which the dissipation due to friction equals the energy supplied by the oscillator. E)  Whether it obeys the conservation of energy principle depends on the tension in the string. A standing wave is created by oscillating a taut string at a frequency that corresponds to one of the resonant frequencies. The amplitude of the antinodes is very much larger than the amplitude of the oscillator. Does this violate the conservation of energy principle? Explain why.


A) Yes, since E is proportional to amplitude squared.
B) Yes, since there is large kinetic energy of the string, and this is much bigger than the energy from the oscillator.
C) No, energy from waves does not obey the conservation of energy principle in the first place.
D) No, the energy at the antinodes builds up after the first few cycles, after which the dissipation due to friction equals the energy supplied by the oscillator.
E) Whether it obeys the conservation of energy principle depends on the tension in the string.

F) A) and E)
G) B) and E)

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A particle is subject to a wave motion. Its distance from the equilibrium position at any particular time is called its


A) amplitude.
B) displacement.
C) phase.
D) wavelength.
E) period.

F) All of the above
G) C) and D)

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The electronic music synthesizer is based on the results of


A) harmonic synthesis.
B) overtones.
C) tone quality.
D) Fourier analysis.
E) all of these factors.

F) A) and C)
G) D) and E)

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The equation that gives the particle displacement of a medium in which there is a simple harmonic progressive wave is , where the units are SI. At t = 2 s, the velocity of a particle at x = 10 m is


A) 0.
B) 2 m/s.
C) 4/p m/s.
D) 4 m/s.
E) 8 m/s.

F) B) and E)
G) A) and D)

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A string fixed at both ends is driven by a tuning fork to produce standing waves. If the tension in the string is increased,


A) the frequency increases.
B) the frequency decreases and the wave velocity remains constant.
C) the wavelength decreases.
D) the wave velocity increases.
E) the wave velocity decreases.

F) B) and E)
G) A) and B)

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  From the figure above, you can conclude that A)  the medium to the left of the boundary is denser than the medium to the right. B)  the medium to the right of the boundary is denser than the medium to the left. C)  the pulse is initially traveling from right to left. D)  the wave has lost energy as a result. E)  None of these is correct. From the figure above, you can conclude that


A) the medium to the left of the boundary is denser than the medium to the right.
B) the medium to the right of the boundary is denser than the medium to the left.
C) the pulse is initially traveling from right to left.
D) the wave has lost energy as a result.
E) None of these is correct.

F) A) and B)
G) All of the above

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