# Quiz 16: Superposition and Standing Waves

Physics & Astronomy

Q 1Q 1

The interference of waves refers to the
A) slowing down of one wave in the presence of another.
B) resultant disturbance of two or more waves at every point in the medium.
C) change in wavelength that occurs when two waves cross one another.
D) phase change of 180º that occurs on reflection of a wave at a fixed end.
E) ability of waves to go around corners.

Free

Multiple Choice

B

Q 2Q 2

In graph A, two waves are shown at a given instant. What is the number of the curve in graph B that represents the wave resulting from the superposition of the two waves in A at this instant?
A) 1
B) 2
C) 3
D) The resultant is zero for all values of x.
E) None of these represent the wave.

Free

Multiple Choice

C

Q 3Q 3

Sketch A shows two identical pulses traveling in opposite directions along a string, each with a velocity of 1.0 cm/s. After 4.0 s, the string will look like which of the other sketches?
A) 1
B) 2
C) 3
D) 4
E) 5

Free

Multiple Choice

B

Q 4Q 4

Two wave trains of the same frequency are traveling in opposite directions down a string. When they meet, these wave trains will not
A) be described by the principle of superposition.
B) reflect from each other.
C) pass through one another.
D) continue to carry energy.
E) remain transverse.

Free

Multiple Choice

Q 5Q 5

Tuning fork A has a frequency of 440 Hz. When A and a second tuning fork B are struck simultaneously, four beats per second are heard. When a small mass is added to one of the tines of B, the two forks struck simultaneously produce two beats per second. The original frequency of tuning fork B was
A) 448 Hz
B) 444 Hz
C) 438 Hz
D) 436 Hz
E) 432 Hz

Free

Multiple Choice

Q 6Q 6

The air columns in two identical pipes vibrate at frequencies of 150 Hz. The percentage of change needed in the length of one of the pipes to produce 3 beats per second is
A) 1%
B) 2%
C) 3%
D) 4%
E) 5%

Free

Multiple Choice

Q 7Q 7

Two loudspeakers S

_{1}and S_{2}, 3.0 m apart, emit the same single-frequency tone in phase at the speakers. A listener L directly in front of speaker S_{1}notices that the intensity is a minimum when she is 4.0 m from that speaker (see figure). What is the lowest frequency of the emitted tone? The speed of sound in air is 340 m/s. A) 85 Hz B) 0.17 kHz C) 0.26 kHz D) 0.34 kHz E) 0.51 kHzFree

Multiple Choice

Q 8Q 8

If two identical waves with the same phase are added, the result is
A) a wave with the same frequency but twice the amplitude.
B) a wave with the same amplitude but twice the frequency.
C) a wave with zero amplitude.
D) a wave with zero frequency.
E) This problem cannot be solved without knowing the wavelengths of the two waves.

Free

Multiple Choice

Q 9Q 9

Two loudspeakers S

_{1}and S_{2}, 3.0 m apart, emit the same single-frequency tone in phase at the speakers. A listener directly in front of speaker S_{1}notices that the intensity is a minimum when she is 4.0 m from that speaker (see figure). The listener now walks around speaker S_{1}in an arc of a circle, staying 4.0 m from that speaker but increasing her distance from the other speaker. How far is she from speaker S_{2}when she notices the first maximum in the sound intensity? The speed of sound in air is 340 m/s. A) 4.5 m B) 5.0 m C) 5.5 m D) 6.0 m E) 6.5 mFree

Multiple Choice

Q 10Q 10

If two identical waves with a phase difference of 6 are added, the result is
A) a wave with the same frequency but twice the amplitude.
B) a wave with the same amplitude but twice the frequency.
C) a wave with zero amplitude.
D) a wave with zero frequency.
E) This problem cannot be solved without knowing the wavelengths of the two waves.

Free

Multiple Choice

Q 11Q 11

If two identical waves with a phase difference of 3 are added, the result is
A) a wave with the same frequency but twice the amplitude.
B) a wave with the same amplitude but twice the frequency.
C) a wave with zero amplitude.
D) a wave with an intensity equal to the sum of the intensities of the two waves.
E) This problem cannot be solved without knowing the wavelengths of the two waves.

Free

Multiple Choice

Q 12Q 12

What is the phase difference at any given instant between two points on a wave which are 1.52 m apart if the wavelength of the wave is 2.13 m?
A) 0.430 rad
B) 2.70 rad
C) 4.48 rad
D) 44.0 rad
E) 119 rad

Free

Multiple Choice

Q 13Q 13

A wave on a string has a frequency of 100 Hz and travels at a speed of 24 m/s. The minimum distance between two points with a phase difference of 60º is
A) 0.040 m
B) 0.12 m
C) 0.14 m
D) 0.24 m
E) 25 m

Free

Multiple Choice

Q 14Q 14

Two waves with the same frequency and wavelength but with different amplitudes are added. If A

_{1}= 2A_{2}and the waves are 180º out of phase, then the amplitude of the resultant wave is A) zero. B) the same as A_{1}. C) the same as A_{2}. D) equal to A_{1}+ A_{2}. E) coherent.Free

Multiple Choice

Q 15Q 15

Two whistles produce sounds with wavelengths 3.40 m and 3.30 m. What is the beat frequency produced? (the speed of sound is 340 m/s)
A) 0.1 Hz
B) 1.0 Hz
C) 2.0 Hz
D) 3.0 Hz
E) 4.0 Hz

Free

Multiple Choice

Q 16Q 16

Middle C on a piano has a frequency of 262 Hz. Sometimes it is said that middle C is actually 2

^{8}= 256 Hz, and tuning forks are made with this frequency. How many beats per second would be heard if such a tuning fork were sounded simultaneously with the middle C of a (well-tuned) piano? A) 3 B) 6 C) 12 D) 4 E) 8Free

Multiple Choice

Q 17Q 17

A violinist is tuning the A string on her violin by listening for beats when this note is played simultaneously with a tuning fork of frequency 440 Hz. She hears a beat frequency of 4 Hz. She notices that, when she increases the tension in the string slightly, the beat frequency decreases. What was the frequency of the mistuned A string?
A) 448 Hz
B) 444 Hz
C) 436 Hz
D) 432 Hz
E) 438 Hz

Free

Multiple Choice

Q 18Q 18

Two trumpet players are both playing a pitch with a frequency of 440 Hz, corresponding to the musical pitch A above middle C. However, one of the trumpet players is marching away from you so that you hear a beat frequency of 4 Hz from the two trumpets. With what speed is the departing trumpet player moving away from you? (The speed of sound in air is 340 m/s)
A) 3.12 m/s
B) 3.09 m/s
C) 3.06 m/s
D) 3.00 m/s
E) 2.95 m/s

Free

Multiple Choice

Q 19Q 19

When a piano tuner strikes both the A above middle C on the piano and a 440 Hz tuning fork, he hears 4 beats each second. The frequency of the piano's A is
A) 440 Hz
B) 444 Hz
C) 880 Hz
D) 436 Hz
E) either 436 Hz or 444 Hz

Free

Multiple Choice

Q 20Q 20

Two tones of equal amplitude but slightly different frequencies are emitted by a sound source. This gives rise to
A) standing waves.
B) destructive interference.
C) constructive interference.
D) beats.
E) amplification.

Free

Multiple Choice

Q 21Q 21

At P

_{1}_{,}the waves from sources S_{1}and S_{2}shown in the figure A) are out of phase. B) have a path difference of one wavelength. C) have a path difference of two wavelengths. D) are interfering destructively. E) None of these is correct.Free

Multiple Choice

Q 22Q 22

At P

_{2}the waves from sources S_{1}and S_{2}shown in the figure A) are in phase. B) have a path difference of one wavelength. C) have a path difference of one-half wavelength. D) are interfering constructively. E) None of these is correct.Free

Multiple Choice

Q 23Q 23

The sources S

_{1}and S_{2}are coherent sources, and the circular arcs represent wave crests. The position that corresponds to a path difference of two wavelengths is A) 1 B) 2 C) 3 D) 4 E) 5Free

Multiple Choice

Q 24Q 24

One source of sound is at A and another is at B. The two sources are in phase. The distance AB = 10.0 m. The frequency of the sound waves from both sources is 1000 Hz, and both have the same amplitude. The speed of sound in air is 330 m/s. A receiver is at point C, and AB is perpendicular to AC. The greatest distance AC for which the signal at C is a minimum is
A) 33.0 cm
B) 152 m
C) 330 m
D) 303 m
E) 100 m

Free

Multiple Choice

Q 25Q 25

The figure shows two waves traveling in the positive-x direction. The amplitude of the resultant wave is
A) 2.0 mm
B) 1.8 mm
C) 1.4 mm
D) 1.0 mm
E) 0.83 mm

Free

Multiple Choice

Q 26Q 26

The figure shows two waves traveling in the positive-x direction. The phase difference between these two waves is
A) radians.
B) /2 radians.
C) /4 radians.
D) /8 radians.
E) /16 radians.

Free

Multiple Choice

Q 27Q 27

The figure shows two waves traveling in the positive-x direction. The phase difference between these two waves is
A) radians.
B) /2 radians.
C) /4 radians.
D) /8 radians.
E) /16 radians.

Free

Multiple Choice

Q 28Q 28

The figure shows two waves traveling in the positive-x direction. The amplitude of the resultant wave is
A) 2.0 mm
B) 1.8 mm
C) 1.4 mm
D) 1.0 mm
E) zero

Free

Multiple Choice

Q 29Q 29

The figure shows two waves traveling in the positive-x direction. The amplitude of the resultant wave is closest to
A) 2.0 mm
B) 1.8 mm
C) 1.4 mm
D) 1.0 mm
E) zero

Free

Multiple Choice

Q 30Q 30

The figure shows two waves traveling in the positive-x direction. The phase difference between these two waves is closest to
A) 3.1 radians.
B) 1.6 radians.
C) 1.1 radians.
D) 2.4 radians.
E) 0.2 radians.

Free

Multiple Choice

Q 31Q 31

The figure shows two waves traveling in the positive-x direction. The phase difference between these two waves is closest to
A) 1.0 radians.
B) 1.5 radians.
C) 2.0 radians.
D) 2.5 radians.
E) 3.0 radians.

Free

Multiple Choice

Q 32Q 32

The figure shows two waves traveling in the positive-x direction. The amplitude of the resultant wave is closest to
A) 2.0 mm
B) 1.8 mm
C) 1.4 mm
D) 1.0 mm
E) zero

Free

Multiple Choice

Q 33Q 33

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

Free

Multiple Choice

Q 34Q 34

Two wave trains travel on a string under a constant tension T. Which of the following statements is NOT correct?
A) The two waves can have different speed.
B) The two waves can have different frequency.
C) The two waves can have different wavelength.
D) The superposition principle applies for the two waves.
E) At any point on the string, the resultant amplitude is the algebraic sum of the amplitudes of the two waves.

Free

Multiple Choice

Q 35Q 35

Two sound waves, one wave is given by y

_{1}= p_{o}sin (kx - t) and the other by y_{2}= p_{o}sin (kx - t + /2). The amplitude resulting from the interference of the two waves is A) 2p_{o}_{ }B) C) 1.25p_{o}_{ }D) E) 0Free

Multiple Choice

Q 36Q 36

Two sound waves, one wave is given by y

_{1}= p_{o}sin (kx - t) and the other by y_{2}= p_{o}sin (kx - t + /4). The phase constant resulting from the interference of the two waves is A) /8 B) /4 C) /2 D) E) 0Free

Multiple Choice

Q 37Q 37

Two sound waves, one wave is given by y

_{1}= p_{o}sin (_{}t), and the other by y_{2}= p_{o}sin (_{}t), where _{1}differs from _{2}by a rad/s. The maximum sound intensity of the beat frequency is A) 0 A) p_{o}^{2}B) 2p_{o}^{2}C) 4p_{o}^{2}D) 8p_{o}^{2}Free

Multiple Choice

Q 38Q 38

Two sources are said to be coherent if
A) they are of the same frequency and has a phase of zero.
B) they are of the same frequency and maintain a constant non-zero phase.
C) they are of the same intensity but different frequency and has a phase of zero.
D) they are of the same intensity but different frequency and maintain a constant non-zero phase.
E) (A) and (B)

Free

Multiple Choice

Q 39Q 39

The figure represents a string of length L, fixed at both ends, vibrating in several harmonics. The 4th harmonic is shown in
A) 1
B) 2
C) 3
D) 4
E) 5

Free

Multiple Choice

Q 40Q 40

The figure represents a string of length L, fixed at both ends, vibrating in several harmonics. The 3rd harmonic is shown in
A) 1
B) 2
C) 3
D) 4
E) 5

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Multiple Choice

Q 41Q 41

The figure represents a wire of length L, fixed at both ends, vibrating in several harmonics. The 7th harmonic is shown in
A) 1
B) 2
C) 3
D) 4
E) 5

Free

Multiple Choice

Q 42Q 42

The figure represents a wire of length L, fixed at both ends, vibrating in several harmonics. The 3rd harmonic is shown in
A) 1
B) 2
C) 3
D) 4
E) 5

Free

Multiple Choice

Q 43Q 43

One wave moves to the right and a second wave (reflected) moves to the left to form a stationary wave. At which point(s) does the stationary wave have a node?
A) 1
B) 3 and 5
C) 2
D) 4 and 6
E) 2, 4, and 6

Free

Multiple Choice

Q 44Q 44

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 is set up in the string. One will observe a node at position
A) 1
B) 2
C) 3
D) 4
E) 5

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Multiple Choice

Q 45Q 45

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

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Multiple Choice

Q 46Q 46

The two progressive waves are moving with equal velocities and wavelengths but in opposite directions in the string. Which of the following gives all of the points that will be nodes in the resultant standing wave?
A) 2, 4, 6, 8, and 10
B) 2, 6, and 10
C) 1, 5, and 9
D) 3 and 7
E) 1, 3, 5, 7, and 9

Free

Multiple Choice

Q 47Q 47

A string whose length is 1 m is fixed at both ends and vibrates according to the equation
Y(x, t) = 0.04 sin x cos 2t
Where the units are SI. The total number of nodes exhibited by the string is
A) 1
B) 2
C) 3
D) 4
E) 5

Free

Multiple Choice

Q 48Q 48

If the amplitude of a standing wave is doubled, the energy in the wave increases by a factor of
A)
B)
C) 1
D) 2
E) 4

Free

Multiple Choice

Q 49Q 49

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)

Free

Multiple Choice

Q 50Q 50

The fundamental frequency of a vibrating string is f

_{1}. If the tension in the string is doubled, the fundamental frequency becomes A) f_{1}/2 B) C) f_{1 }D) E) 2f_{1 }Free

Multiple Choice

Q 51Q 51

The fundamental frequency of a vibrating string is f

_{1}. If the tension in the string is increased by 50% while the linear density is held constant, the fundamental frequency becomes A) f_{1 }B) 1.2f_{1 }C) 1.5f_{1 }D) 1.7f_{1 }E) 2f_{1 }Free

Multiple Choice

Q 52Q 52

The fundamental frequency of a vibrating string is f

_{1}. If the tension in the string is decreased by 50% while the linear density is held constant, the fundamental frequency becomes A) 0.5f_{1 }B) 0.7f_{1 }C) 0.9f_{1 }D) f_{1 }E) None of these is correct.Free

Multiple Choice

Q 53Q 53

The fundamental frequency of a vibrating string is f

_{1}. If the tension in the string is quadrupled while the linear density is held constant, the fundamental frequency becomes A) f_{1 }B) 1.2f_{1 }C) 1.5f_{1 }D) 1.7f_{1 }E) 2f_{1 }Free

Multiple Choice

Q 54Q 54

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.

Free

Multiple Choice

Q 55Q 55

Which of the following equations represents a standing wave? (The symbols have their usual meaning.)
A)
B)
C)
D)
E) (B) and (D)

Free

Multiple Choice

Q 56Q 56

A standing wave is shown in the figure on the right. If the period of the wave is T, the shortest time it takes for the wave to go from the solid curve to the dashed curve is
A) T/4
B) T/3
C) T/2
D) 3T/4
E) None of these is correct.

Free

Multiple Choice

Q 57Q 57

A string of linear density and length L is under a constant tension T = mg. One end of the string is attached to a tunable harmonic oscillator. A resonant standing wave is observed
A) at any frequency.
B) when the frequency where n = 1, 2, 3, ...
C) when the frequency where n = 1, 2, 3, ...
D) when the frequency where n = 1, 2, 3, ...and v

_{s}is the speed of sound. E) unable to tellFree

Multiple Choice

Q 58Q 58

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.

Free

Multiple Choice

Q 59Q 59

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.

Free

Multiple Choice

Q 60Q 60

Four pendulums are hung from a light rod that is free to rotate about its long axis. The pendulums have lengths L, 2L, L/2 and L, and masses m, m/2, 2m and 4m respectively. Pendulum 1 is set to swing at its natural frequency. Which of the other three will, over time, also oscillate at the same frequency?
A) (2)
B) (3)
C) (4)
D) (2) and (3)
E) all three

Free

Multiple Choice

Q 61Q 61

In a vibrating-string experiment, three loops are observed between points A and B when the mass on one end of the string is 100 g. The number of loops between A and B can be changed to two by replacing the 100-g mass with a mass of
A) 150 g
B) 225 g
C) 44.4 g
D) 66.7 g
E) 300 g

Free

Multiple Choice

Q 62Q 62

A string 2.0 m long has a mass of 2.4 10

^{-2}kg. When fixed at both ends, it vibrates with a fundamental frequency of 150 Hz. The speed of a transverse wave in the string is A) 3.6 m/s B) 75 m/s C) 0.30 km/s D) 0.60 km/s E) 0.63 km/sFree

Multiple Choice

Q 63Q 63

A string 2.0 m long has a mass of 2.4 10

^{-2}kg. When fixed at both ends, it vibrates with a fundamental frequency of 150 Hz. The frequency of the third harmonic of this fundamental is A) 50 Hz B) 75 Hz C) 0.15 kHz D) 0.45 kHz E) 1.1 kHzFree

Multiple Choice

Q 64Q 64

A stationary wave of amplitude A and period T exists in a rope. At a particular instant, the configuration of the rope is as shown. At an instant T later, the configuration of the rope is
A) 1
B) 2
C) 3
D) 4
E) 5

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Multiple Choice

Q 65Q 65

A string is connected to a tuning fork whose frequency is 80.0 Hz and is held under tension by 0.500 kg. The tuning fork causes the string to vibrate as shown. The mass per unit length for the string is
A) 9.45 10

^{-4}kg/m B) 6.80 10^{-3}kg/m C) 4.34 kg/m D) 6.00 10^{-3}kg/m E) 3.85 10^{-2}kg/mFree

Multiple Choice

Q 66Q 66

A stretched string is fixed at points 1 and 5. When it is vibrating at the second harmonic frequency, the nodes of the standing wave are at points
A) 1 and 5.
B) 1, 3, and 5.
C) 1 and 3.
D) 2 and 4.
E) 1, 2, 3, 4, and 5.

Free

Multiple Choice

Q 67Q 67

A stretched string is fixed at points 1 and 5. When it is vibrating in its first harmonic frequency, the nodes are at points
A) 1 and 5 only.
B) 1, 3, and 5.
C) 2 and 4.
D) 2, 3, and 4.
E) 1, 2, 3, 4, and 5.

Free

Multiple Choice

Q 68Q 68

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.

Free

Multiple Choice

Q 69Q 69

The figure shows a standing wave in a pipe that is closed at one end. The frequency associated with this wave pattern is called the
A) first harmonic.
B) second harmonic.
C) third harmonic.
D) fourth harmonic.
E) fifth harmonic.

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Multiple Choice

Q 70Q 70

Of the sound sources shown, that which is vibrating with its first harmonic is
A) the whistle.
B) the organ pipe.
C) the vibrating string.
D) the vibrating rod.
E) None of these is correct.

Free

Multiple Choice

Q 71Q 71

Of the sound sources shown, that which is vibrating with its first harmonic is the
A) whistle.
B) organ pipe.
C) vibrating string.
D) vibrating rod.
E) vibrating spring.

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Multiple Choice

Q 72Q 72

When an organ pipe, which is closed at one end only, vibrates with a frequency that is three times its fundamental (first harmonic) frequency,
A) the sound produced travels at three times its former speed.
B) the sound produced is its fifth harmonic.
C) beats are produced.
D) the sound produced has one-third its former wavelength.
E) the closed end is a displacement antinode.

Free

Multiple Choice

Q 73Q 73

The air in a closed organ pipe vibrates as shown. The length of the pipe is 3.0 m. The frequency of vibration is 80 Hz. The speed of sound in the pipe is approximately
A) 80 m/s
B) 0.16 km/s
C) 0.24 km/s
D) 0.32 km/s
E) 0.96 km/s

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Multiple Choice

Q 74Q 74

A vibrating tuning fork of frequency 640 Hz is held above a tube filled with water. Assume the speed of sound to be 330 m/s. As the water level is lowered, consecutive maxima in intensity are observed at intervals of about
A) 12.9 cm
B) 19.4 cm
C) 25.8 cm
D) 51.7 cm
E) 194 cm

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Multiple Choice

Q 75Q 75

A vibrating tuning fork of frequency 1080 Hz is held above a tube filled with water. Assume the speed of sound to be 330 m/s. As the water level is lowered, consecutive maxima in intensity are observed at intervals of about
A) 7.65 cm
B) 15.3 cm
C) 23.0 cm
D) 30.6 cm
E) 53.6 cm

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Multiple Choice

Q 76Q 76

The air column in an organ pipe, which is closed at one end, is vibrating in such a way as to produce the second harmonic. A pressure node and displacement node, respectively, occur at
A) 1 and 3
B) 1 and 5
C) 7 and 4
D) 7 and 5
E) 5 and 3

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Multiple Choice

Q 77Q 77

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.

Free

Multiple Choice

Q 78Q 78

On a standing-wave pattern, the distance between two consecutive nodes is d. The wavelength is
A) d/2
B) d
C) 3d/2
D) 2d
E) 4d

Free

Multiple Choice

Q 79Q 79

A stretched string of length L, fixed at both ends, is vibrating in its third harmonic. How far from the end of the string can the blade of a screwdriver be placed against the string without disturbing the amplitude of the vibration?
A) L/6
B) L/4
C) L/5
D) L/2
E) None of these is correct.

Free

Multiple Choice

Q 80Q 80

In a pipe that is open at one end and closed at the other and that has a fundamental frequency of 256 Hz, which of the following frequencies cannot be produced?
A) 768 Hz
B) 1.28 kHz
C) 5.12 kHz
D) 19.7 kHz
E) all of these can be produced

Free

Multiple Choice

Q 81Q 81

The fundamental frequency of a pipe that has one end closed is 256 Hz. When both ends of the same pipe are opened, the fundamental frequency is
A) 64.0 Hz
B) 128 Hz
C) 256 Hz
D) 512 Hz
E) 1.02 kHz

Free

Multiple Choice

Q 82Q 82

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) /2, , and 3/2
D) L/v, 2L/v, and 3L/v
E) /3, 2/3, and 3/3

Free

Multiple Choice

Q 83Q 83

Standing waves exist in a string of length L that is fixed at one end and free at the other. The speed of the waves on the string is v. The three lowest frequencies of vibration are
A) v/4L, v/2L, and 3v/4L
B) v/2L, v/L, and 3v/2L
C) /4, /2, and 3/4
D) v/4L, 3v/4L, and 5v/4L
E) /3, 2/3, and 3/3

Free

Multiple Choice

Q 84Q 84

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) /2, , and 3/2
D) L/v, 2L/v, and 3L/v
E) /3, 2/3, and 3/3

Free

Multiple Choice

Q 85Q 85

The standing waves in air in a pipe of length L that is open at one end and closed at the other have a speed v. The frequencies of the three lowest harmonics are
A) v/4L, v/2L, and 3v/4L
B) v/2L, v/L, and 3v/2L
C) /4, /2, and 3/4
D) v/4L, 3v/4L, and 5v/4L
E) /3, 2/3, and 3/3

Free

Multiple Choice

Q 86Q 86

A 1.00 m string fixed at both ends vibrates in its fundamental mode at 440 Hz. What is the speed of the waves on this string?
A) 220 m/s
B) 440 m/s
C) 660 m/s
D) 880 m/s
E) 1.10 km/s

Free

Multiple Choice

Q 87Q 87

The human vocal tract can be thought of as a tube that is open at one end. If the length of this tube is 17 cm (about average for an adult male), what are the lowest two harmonics?
A) 500 Hz, 1500 Hz
B) 500 Hz, 1000 Hz
C) 1000 Hz, 2000 Hz
D) 1000 Hz, 3000 Hz
E) 1500 Hz, 2500 Hz

Free

Multiple Choice

Q 88Q 88

For a tube of length 57.0 cm that is open at both ends, what is the frequency of the fundamental mode? (the speed of sound in air is 340 m/s)
A) 149 Hz
B) 447 Hz
C) 596 Hz
D) 298 Hz
E) 746 Hz

Free

Multiple Choice

Q 89Q 89

A string fixed at both ends is 50.0 cm long and has a tension that causes the frequency of its fundamental to be 262 Hz. If the tension is increased by 4%, what does the fundamental frequency become?
A) 252 Hz
B) 257 Hz
C) 264 Hz
D) 267 Hz
E) 272 Hz

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Multiple Choice

Q 90Q 90

A clarinet, which is essentially a tube that is open at one end, is properly tuned to concert A (440 Hz) indoors, where the temperature is 20ºC and the speed of sound is 340 m/s. The musician then takes the instrument to play an outdoor concert, where the temperature is 0ºC and the speed of sound is 331 m/s. What is the frequency of the A played on the cold clarinet? (Ignore any thermal changes in the body of the clarinet itself.)
A) 417 Hz
B) 428 Hz
C) 434 Hz
D) 445 Hz
E) 451 Hz

Free

Multiple Choice

Q 91Q 91

Sound has a velocity of 335 m/s in air. For an air column that is closed at both ends to resonate to a frequency of 528 Hz, the length of the air column could be
A) 79.2 cm
B) 55.5 cm
C) 47.5 cm
D) 31.7 cm
E) 15.8 cm

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Multiple Choice

Q 92Q 92

The sound wave in an organ tube has a wavelength that is equal to the distance between
A) A and B.
B) A and C.
C) the nodes farthest apart.
D) the antinodes farthest apart.
E) None of these is correct.

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Multiple Choice

Q 93Q 93

The third harmonic of a tube closed at one end is 735 Hz. If the speed of sound in air is 335 m/s, the length of the tube must be
A) 11.6 cm
B) 22.9 cm
C) 34.1 cm
D) 45.7 cm
E) 57.3 cm

Free

Multiple Choice

Q 94Q 94

The ratio of the fundamental frequency (first harmonic) of an open pipe to that of a closed pipe of the same length is
A) 2:1
B) 7:8
C) 4:5
D) 3:2
E) 1:2

Free

Multiple Choice

Q 95Q 95

The wave function y(x,t) for a standing wave on a string fixed at both ends is given by y(x,t) = 0.080 sin 6.0x cos 600t where the units are SI. The amplitudes of the traveling wave that result in this standing wave are
A) 0.04 m
B) 0.08 m
C) 0.02 m
D) 0.16 m
E) impossible to tell given this information about the standing wave.

Free

Multiple Choice

Q 96Q 96

The wave function y(x,t) for a standing wave on a string fixed at both ends is given by y(x,t) = 0.080 sin 6.0x cos 600t where the units are SI. The wavelength of this wave is
A) 6.00 m
B) 1.05 m
C) 600 m
D) 0.010 m
E) impossible to tell given this information about the standing wave.

Free

Multiple Choice

Q 97Q 97

The wave function y(x,t) for a standing wave on a string fixed at both ends is given by y(x,t) = 0.080 sin 6.0x cos 600t where the units are SI. The speed of the traveling waves that result in this standing wave is
A) 6.00 m
B) 1.05 m
C) 600 m
D) 0.010 m
E) impossible to tell given this information about the standing wave.

Free

Multiple Choice

Q 98Q 98

The wave function y(x,t) for a standing wave on a string fixed at both ends is given by y(x,t) = 0.080 sin 6.0x cos 600t where the units are SI. The distance between successive nodes on the string is
A) 0.24 m
B) 0.08 m
C) 0.02 m
D) 0.52 m
E) impossible to tell given this information about the standing wave.

Free

Multiple Choice

Q 99Q 99

A string with mass density equal to 0.0025 kg/m is fixed at both ends and at a tension of 290 N. Resonant frequencies are found at 558 Hz and the next one at 744 Hz. What is the fundamental frequency of the string?
A) 558 Hz
B) 372 Hz
C) 93 Hz
D) 186 Hz
E) none of the above

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Multiple Choice

Q 100Q 100

A string with mass density equal to 0.0025 kg/m is fixed at both ends and at a tension of 290 N. Resonant frequencies are found at 558 Hz and the next one at 744 Hz. To what harmonic does the 558 Hz resonance correspond?
A) 1
B) 2
C) 3
D) 4
E) 5

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Multiple Choice

Q 101Q 101

A string with mass density equal to 0.0025 kg/m is fixed at both ends and at a tension of 290 N. Resonant frequencies are found at 558 Hz and the next one at 744 Hz. What is the length of the wire?
A) 0.8 m
B) 1.6 m
C) 3.2 m
D) 1.2 m
E) 0.4 m

Free

Multiple Choice

Q 102Q 102

A wire of mass 1.1 g is under a tension of 100 N. If its third overtone is at a frequency of 750 Hz, calculate the length of the wire.
A) 72 cm
B) 101 cm
C) 36 cm
D) 65 cm
E) None of the above

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Multiple Choice

Q 103Q 103

A vibrating tuning fork is held above a tube filled with water. The first two resonances occur when the water level is lowered by 14.2 cm and 44.2 cm from the top of the tube. If there is a small end correction that adds a small extra length L? to the effective length of the air column, calculate the frequency of the tuning fork. Assume the speed of sound to be 330 m/s.
A) 560 Hz
B) 581 Hz
C) 550 Hz
D) 1100 Hz
E) 1120 Hz

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Multiple Choice

Q 104Q 104

A vibrating tuning fork of 850 Hz is held above a tube filled with water. The first and third resonances occur when the water level is lowered by 8.8 cm and 47.6 cm from the top of the tube. If there is a small end correction that adds a small extra length L to the effective length of the air column, calculate L. Assume the speed of sound to be 330 m/s.
A) 0.2 cm
B) 0.9 cm
C) 0.4 cm
D) 0.6 cm
E) 1.1 cm

Free

Multiple Choice

Q 105Q 105

A vibrating tuning fork of 725 Hz is held above a tube filled with water. Successive resonances are heard when the water level is lowered by 11.5 cm and 34.5 cm from the top of the tube. Calculate a value for the speed of sound. (Hint: remember the small end correction L at the top of the tube.)
A) 333 m/s
B) 343 m/s
C) 325 m/s
D) 315 m/s
E) 338 m/s

Free

Multiple Choice

Q 106Q 106

Two pipes closed at one end of length L

_{1}and L_{2}are excited at their resonant frequencies. If the beat period is B_{f}Hz, then the velocity of sound is given by: A) B_{f} L_{1} L_{2}/ (4L_{1} 4L_{2}) B) 4 B_{f} L_{1} L_{2}/ (4L_{1} 4L_{2}) C) 16 B_{f} L_{1} L_{2}/ (4L_{1}+ 4L_{2}) D) 4 B_{f} L_{1} L_{2}/ (L_{1} L_{2}) E) 4 B_{f} L_{1} L_{2}/ (L_{1}+ L_{2})Free

Multiple Choice

Q 107Q 107

A vibrating tuning fork of 300 Hz is held above a tube filled with water. The first resonance is heard when the water level is lowered by 26.1 cm. A second tuning fork of 400 Hz is held above the tube, and its first resonance occurs when the water level is lowered by 19.3 cm from the top. Calculate a value for the speed of sound. (Hint: remember the small end correction L at the top of the tube.)
A) 333 m/s
B) 343 m/s
C) 325 m/s
D) 315 m/s
E) 338 m/s

Free

Multiple Choice

Q 108Q 108

A guitar string of length 105 cm is in resonance with a tuning fork of frequency f. Using the fret board the length of the string is shortened by 1.5 cm while keeping the tension in the string constant. Now a beat frequency of 10 Hz is heard between the string and the tuning fork. What is the frequency of the tuning fork?
A) 230 Hz
B) 1380 Hz
C) 345 Hz
D) 690 Hz
E) none of the above

Free

Multiple Choice

Q 109Q 109

Wire A is the same mass per unit length as wire B. However wire A is twice as long as wire B and has three times as much tension on it. Calculate the fundamental frequency of wire A divided by wire B.
A) 0.87
B) 0.66
C) 0.43
D) 0.75
E) 1.50

Free

Multiple Choice

Q 110Q 110

What is the third harmonic of an open-both-ends organ pipe of length 1.5 m? Assume the speed of sound to be 340 m/s.
A) 229 Hz
B) 340 Hz
C) 457 Hz
D) 686 Hz
E) none of the above

Free

Multiple Choice

Q 111Q 111

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

Free

Multiple Choice

Q 112Q 112

Two identical loudspeakers are driven in phase by the same amplifier. The speakers are positioned a distance of 3.2 m apart. A person stands 4.1 m away from one speaker and 4.8 m away from the other. Calculate the second lowest frequency that results in destructive interference at the point where the person is standing. Assume the speed of sound to be 340 m/s.
A) 245 Hz
B) 735 Hz
C) 1225 Hz
D) 490 Hz
E) 1470 Hz

Free

Multiple Choice

Q 113Q 113

A pipe produces successive harmonics at 300 Hz and 350 Hz. Calculate the length of the pipe and state whether it is closed at one end or not. Assume the speed of sound to be 340 m/s.
A) 1.7 m
Closed one end
B) 3.4 m
Open both ends
C) 4.0 m
Closed one end
D) 8.0 m
Closed one end
E) 4.0 m
Open both ends

Free

Multiple Choice

Q 114Q 114

The reason we can tell the difference between a trumpet and a clarinet when they both play the same pitch is that they have
A) the same overtones.
B) the same harmonics.
C) different fundamental frequencies.
D) different waveforms.
E) harmonic syntheses.

Free

Multiple Choice

Q 115Q 115

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.

Free

Multiple Choice

Q 116Q 116

A string with length L is fixed on both ends. If

_{o}= 2L and f_{o}= v/_{}, the wave function for the harmonic shown is A) B) C) D) E)Free

Multiple Choice

Q 117Q 117

The complex wave whose frequency spectrum is shown in the figure is made up of waves whose frequencies are
A) 1, 2, and 4.
B) 100, 200, and 400.
C) 100, 100, and 400.
D) 1 and 4.
E) 100 and 400.

Free

Multiple Choice

Q 118Q 118

The complex wave whose frequency spectrum is shown in the figure is made up of waves whose relative amplitudes are
A) 1, 2, and 4.
B) 100, 200, and 400.
C) 1 and 4.
D) 200 and 400.
E) 1 and 2.

Free

Multiple Choice

Q 119Q 119

The frequency spectrum of the composite wave 1 + 3 + 5 shown is best represented by
A) 1
B) 2
C) 3
D) 4
E) 5

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Multiple Choice

Q 120Q 120

An examination of this frequency spectrum allows you to conclude that
A) the odd harmonics 1 through 19 are present in the composite wave.
B) the even harmonics 2 through 20 are present in the composite wave.
C) the amplitudes of the component waves are equal.
D) the wave form is a simple sinusoid.
E) None of these is correct.

Free

Multiple Choice

Q 121Q 121

The three curves show the harmonics of a pipe that is closed one end and open the other end. The fundamental frequency is f

_{o}. The three harmonics are A) f_{o}, 2f_{o}, 3f_{o}B) f_{o}, 5f_{o}, 7f_{o}C) f_{o}, 4f_{o}, 6f_{o}D) f_{o}, 3f_{o}, 4f_{o}E) f_{o}, 6f_{o}, 8f_{o}Free

Multiple Choice

Q 122Q 122

Use the figure to the right to answer the next problems.
The graph shows three harmonics.
-The frequency spectrum of the composite wave is best represented by
A)
B)
C)
D)
E) None of the above

Free

Multiple Choice

Q 123Q 123

Use the figure to the right to answer the next problems.
The graph shows three harmonics.
-If f

_{o}is the fundamental frequency, the three harmonics and their relative intensities can best be written as A) f_{o}, 2f_{o}, 3f_{o}_{,}and 2:1:0.5 B) f_{o}, 3f_{o}, 5f_{o}_{,}and 2:1:1 C) f_{o}, 3f_{o}, 5f_{o}_{,}and 2:1:0.5 D) f_{o}, 3f_{o}, 4f_{o}_{,}and 2:1:0.5 E) f_{o}, 6f_{o}, 8f_{o}_{,}and 2:1:1Free

Multiple Choice

Q 124Q 124

Use the figure to the right to answer the next problems.
The graph shows a wave pulse of width w = 5 cm and speed v = 100 m/s.
-The duration of the wave pulse is
A) 0.005 s
B) 0.0005 s
C) 0.001 s
D) 0.02 s
E) 0.5 s

Free

Multiple Choice

Q 125Q 125

Use the figure to the right to answer the next problems.
The graph shows a wave pulse of width w = 5 cm and speed v = 100 m/s.
-The range of frequencies is
A) 2000 s

^{ }^{1}B) 200 s^{ }^{1}C) 1000 s^{ }^{1}D) 50 s^{ }^{1}E) 5 s^{ }^{1}Free

Multiple Choice