Deck 15: Wave Motion

Question 1

A string under tension carries a transverse wave traveling at speed v. If the tension in the string is halved and the linear density of the string is quadrupled, what is the wave speed?

A) The wave speed is unchanged.
B) The wave speed is halved.
C) The wave speed is quadrupled.
D) The wave speed decreases to about 71% of v.
E) The wave speed increases by about 41%.

Answer 1

The wave speed decreases to about 71% of v.

Question 2

A general rule for estimating the distance in kilometers between you and a lightning bolt is to count the number of seconds between the time you see the flash and the time you hear the thunder and then divide by

A) 2
B) 3
C) 4
D) 5
E) None of these is correct.

Answer 2

3

Question 3

Which curve best represents the variation of wave velocity with linear density in a vibrating string?

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

Answer 3

1

Question 4

Sound travels at 340 m/s in air and 1500 m/s in water. A sound of 256 Hz is made under water. In the air,

A) the frequency remains the same but the wavelength is shorter.
B) the frequency is higher but the wavelength stays the same.
C) the frequency is lower but the wavelength is longer.
D) the frequency is lower and the wavelength is shorter.
E) both the frequency and the wavelength remain the same.

Question 5

Both particles and waves transfer energy from one location to another. Which of the following statements is true?

A) Both methods of energy transfer follow the conservation of energy principle.
B) Energy transfer by particles follows the conservation of energy principle but waves do not.
C) Energy transfer by waves follows the conservation of energy principle but particles do not.
D) Whether the transfer of energy by a wave follows the conservation of energy principle depends on the speed of the wave.
E) Whether the transfer of energy by a particle follows the conservation of energy principle depends on the speed of the particle.

Question 6

In which of the following is the speed of sound greatest?

A) air
B) water
C) a vacuum
D) wood
E) steel

Question 7

Which curve best illustrates the variation of wave velocity with linear density in a vibrating string?

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

Question 8

Which of the following statements is true?

A) Waves transmit energy but not momentum.
B) Waves transmit momentum but not energy.
C) Waves transmit both energy and momentum.
D) Waves transmit neither energy nor momentum.
E) Waves can transmit either energy or momentum but not both.

Question 9

A longitudinal wave is distinguished from a transverse wave by the fact that in longitudinal waves

A) the particle vibration is parallel to the direction of propagation.
B) the particle vibration is perpendicular to the direction of propagation.
C) energy is transported from one point in space to another point.
D) vibrations occur only in air or water.
E) energy is not transported from one point in space to another point.

Question 10

A string under tension carries a transverse wave traveling at speed v. If the tension in the string is halved, what is the wave speed?

A) The wave speed is unchanged.
B) The wave speed is halved.
C) The wave speed is quadrupled.
D) The wave speed decreases to about 71% of v.
E) The wave speed increases by about 41%.

Question 11

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

Question 12

Which curve best illustrates the variation of wave velocity with tension in a vibrating string?

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

Question 13

A string under tension carries a transverse wave traveling at speed v. If the linear density of the string is halved, what is the wave speed?

A) The wave speed is unchanged.
B) The wave speed is halved.
C) The wave speed is quadrupled.
D) The wave speed decreases to about 71% of v.
E) The wave speed increases by about 41%.

Question 14

A string under tension carries transverse waves traveling at speed v. If the same string is under four times the tension, what is the wave speed?

A) v
B) 2v
C) v/2
D) 4v
E) v/4

Question 15

A piano wire has a tension of 650 N and a mass per unit length of 0.060 g/cm. What is the speed of waves on this wire?

A) 1.0 $\times$ 10² m/s
B) 3.3 $\times$ 10² m/s
C) 1.0 $\times$ 10³ m/s
D) 33 m/s
E) 52 m/s

Question 16

A string under tension carries a transverse wave traveling at speed v. If the linear density of the string is doubled, what is the wave speed?

A) The wave speed is unchanged.
B) The wave speed is halved.
C) The wave speed is quadrupled.
D) The wave speed decreases to about 71% of v.
E) The wave speed increases by about 41%.

Question 17

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

Question 18

During the passage of a longitudinal wave, a particle of the medium

A) remains in a fixed position.
B) moves in a circle.
C) moves at right angles to the direction of propagation.
D) moves forward and backward along the line of propagation.
E) moves forward with the velocity of the wave.

Question 19

Which of the following statements about longitudinal and transverse pressure waves is NOT true?

A) Longitudinal pressure waves can travel through fluids.
B) Transverse pressure waves can travel through fluids.
C) Longitudinal pressure waves can travel through solids.
D) Transverse pressure waves can travel through solids.
E) Both longitudinal and transverse pressure waves transport energy.

Question 20

A string under tension carries a transverse wave traveling at speed v. If the tension in the string is quadrupled and the linear density of the string is doubled, what is the wave speed?

A) The wave speed is unchanged.
B) The wave speed is halved.
C) The wave speed is quadrupled.
D) The wave speed decreases to about 71% of v.
E) The wave speed increases by about 41%.

Question 21

Use the following scenario to answer the next question. A rope of length L and linear mass density $\mu$ is tied to the ceiling on one end. The other end is tied to a spring with spring constant k, and the spring is then attached to the floor, extending it by A.

-The speed of a wave pulse at height h from the spring is

A)
B)
C)
D)
E)

Question 22

The curve that represents the speed of sound in a gas plotted against the kelvin temperature is

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

Question 23

The speed of sound in air at 0ºC is 331 m/s. What is the speed of sound in air at -40ºC?

A) 241 m/s
B) 282 m/s
C) 306 m/s
D) 309 m/s
E) 379 m/s

Question 24

A sound pulsar unit puts out short sound bursts at constant time intervals. This unit also has a receiver to listen to the time delay from an echo from any objects or walls. If the unit is positioned such that the echo time corresponds to the sound burst interval of 0.6 s, find the distance to the reflecting wall. (velocity of sound in air = 331 m/s)

A) 150 m
B) 50.0 m
C) 200 m
D) 100 m
E) none of the above

Question 25

A triangular wave pulse as shown by the blue line can be formed by adding

A) harmonic sine waves with different frequencies and intensities.
B) harmonic cosine waves with different frequencies and intensities.
C) a combination of harmonic sine and cosine waves with different frequencies and intensities.
D) either (A), (B) or (C)
E) it is not possible to form triangular using harmonic waves.

Question 26

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, how thick is layer (2)?

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

Question 27

If the speed of sound is 331 m/s at 0 ^$\circ$ C and at temperature T it is 350 m/s, find T.

A) 1 ^$\circ$ C
B) 16 ^$\circ$ C
C) 32 ^$\circ$ C
D) -16 ^$\circ$ C
E) none of the above

Question 28

Increasing the temperature, expressed in kelvins, in a gas by 125% will produce an increase in the speed of sound in the gas of approximately

A) 25%
B) 18%
C) 12%
D) 9%
E) 4%

Question 29

A stationary ship generates a sound signal at the bow and has a receiver system at the stern of the ship 100 m away. The difference in time between the signal arriving at the stern traveling directly through the air and the signal reflected from the sea bottom is 0.5 second. If the velocity of sound in air is 331 m/s and in water is 1435 m/s, calculate the depth of water below the ship.

A) 1150 m
B) 574 m
C) 359 m
D) 396 m
E) 450 m

Question 30

A string is stretched by a force of 4.0 N. The mass per unit length of the string is 4.0 $\times$ 10^-4 kg/m. A transverse wave would travel along this string with a velocity of approximately

A) 0.80 cm/s
B) 2.0 cm/s
C) 8.0 cm/s
D) 50 m/s
E) 1.0 $\times$ 10² m/s

Question 31

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.

Question 32

In a seismic event, two types of waves are created, a P-wave (longitudinal) and an S-wave (transverse). The waves travel at speeds of 8 km/s and 5 km/s respectively. At a monitoring station, a P-wave is observed 10 s before the S-wave. How far is the seismic activity from the station? Assume that the waves travel in a straight line.

A) 50 km
B) 80 km
C) 30 km
D) 133 km
E) none of the above

Question 33

A stationary ship generates a sound signal at the bow and has a receiver system at the stern of the ship 100 m away. The signal arriving at the stern traveling directly through the air and the signal reflected from the sea bottom arrive at the sensor at the same time. If the velocity of sound in air is 331 m/s and in water is 1435 m/s, calculate the depth of water below the ship.

A) 434 m
B) 422 m
C) 217 m
D) 211 m
E) 192 m

Question 34

The speed of sound in dry air at 20ºC is 343 m/s. The speed of sound in dry air at 80ºC is

A) 86.0 m/s
B) 172 m/s
C) 377 m/s
D) 686 m/s
E) 1.27 km/s

Question 35

A string exactly two meters long has a mass of 10.0 g and is under a tension of 12.5 N. The speed of a transverse wave in this string is

A) 1.58 m/s
B) 15.8 m/s
C) 25.0 m/s
D) 44.7 m/s
E) 50.0 m/s

Question 36

Use the following scenario to answer the next question. A rope of length L and linear mass density $\mu$ is tied to the ceiling on one end. The other end is tied to a spring with spring constant k, and the spring is then attached to the floor, extending it by A.

-The time it takes for a wave pulse to travel from the bottom of the rope to the ceiling is

A)
B)
C)
D)
E)

Question 37

Which of the following function is NOT a possible wave equation? A and c are constants. The other symbols have their usual meaning.

A) y(x,t) = 1/(x - vt)
B) y(x,t) = A e^-vxt/c
C)
D) y(x,t) = A cos (kx) sin (ωt)
E) y(x,t) = A sin(kx + ωt)

Question 38

A wave is traveling with a speed v along the x axis in the positive direction. The upper graph shows the displacement y versus the distance x for a given instant of time. The lower graph shows the displacement y versus the time t for any given point x. From the information in the graphs, what is the wave speed v?

A) 8.0 m/s
B) 4.0 m/s
C) 6.0 m/s
D) There is not enough information to solve the problem.
E) None of these is correct.

Question 39

A string of mass 2.4 $\times$ 10^-3 kg and length 0.60 m vibrates transversely in such a way that its fundamental frequency is 100 Hz. The tension on this string must be approximately

A) 0.16 N
B) 0.32 N
C) 13 N
D) 26 N
E) 58 N

Question 40

Use the following scenario to answer the next question. A rope of length L and linear mass density $\mu$ is tied to the ceiling on one end. The other end is tied to a spring with spring constant k, and the spring is then attached to the floor, extending it by A.

-The tension of the rope at height y from the spring is

A) kA
B) $\mu$ gy
C) $\mu$ gy + kA
D) $\mu$ gy - kA
E) kA - $\mu$ gy

Question 41

As a wave moves to the right in an elastic rope, a sequence of pictures (1 through 6) is taken at intervals of one second. An arrow points out a particle that is attached to the rope. If the width of the picture is 8 cm, this wave has a period of

A) 0.2 s
B) 10 s
C) 3 s
D) 6 s
E) 12 s

Question 42

The average rate at which energy is transmitted along a string depends on

A) the linear density of the string.
B) the square of the angular frequency of the source.
C) the square of the amplitude of the wave.
D) the speed of the wave.
E) all of these factors

Question 43

The graph shows a wave traveling to the right with a velocity of 4 m/s. The equation that best represents the wave is

A) y(x, t) = 2 sin( $\pi$ x/4 - $\pi$ t) m
B) y(x, t) = 2 sin(16 $\pi$ x - 8 $\pi$ t) m
C) y(x, t) = 2 sin( $\pi$ x/4 + $\pi$ t) m
D) y(x, t) = 4 sin( $\pi$ x/4 - $\pi$ t) m
E) y(x, t) = 4 sin(16 $\pi$ x - 8 $\pi$ t) m

Question 44

An equation that gives the particle displacement for a medium in which there is a simple harmonic traveling wave is
Y(x, t) = (2/ $\pi$ ) sin $\pi$ (3x + 2t),
Where x and y are in centimeters and t is in seconds. At t = 2 s the speed of a particle at the location x = 4 cm is

A) 0
B) 2 cm/s
C) 4 cm/s
D) 6 cm/s
E) 8 cm/s

Question 45

In a sinusoidal traveling wave, the distance between two points that differ in phase by 2 $\pi$ radians is the

A) frequency.
B) period.
C) amplitude.
D) phase constant.
E) wavelength.

Question 46

The equation of a traveling wave is
Y(x, t) = 0.02 cos(0.25x - 500t)
Where the units are SI. The velocity of the wave is

A) 4.0 m/s
B) 10 m/s
C) 0.13 km/s
D) 0.50 km/s
E) 2.0 km/s

Question 47

A set of waves has a speed of 4.2 m/s and a frequency of 2.0 Hz. The wavelength is

A) 8.4 m
B) 2.1 m
C) 0.48 m
D) 0.84 m
E) 3.2 m

Question 48

A sinusoidal wave train is moving along a string. The equation giving the displacement as a function of position and time is
Y(x, t) = 0.12 sin 8 $\pi$ (t - x/50),
Where the units are SI. For a particle at x = 5 m when t = 2.4 s, the velocity of the particle is

A) 3.7 cm/s
B) 27 cm/s
C) 93 cm/s
D) 1.6 m/s
E) 3.0 m/s

Question 49

Waves on the surface of a liquid are observed to have a wavelength of 12.9 mm and a speed of 30.9 cm/s. The frequency of the wave motion is

A) 1.8 mHz
B) 24 Hz
C) 42 mHz
D) 2.4 Hz
E) 2.4 mHz

Question 50

A traveling wave passes a point of observation. At this point, the time between successive crests is 0.2 s. Which of the following statements can be justified?

A) The wavelength is 5 m.
B) The frequency is 5 Hz.
C) The velocity of propagation is 5 m/s.
D) The wavelength is 0.2 m.
E) There is not enough information to justify any of these statements.

Question 51

The equation of a transverse wave is
Y(x, t) = 0.02 cos(10 $\pi$ x - 400 $\pi$ t)
Where the units are SI. The velocity of the wave is

A) 0.20 $\pi$ m/s
B) 8 $\pi$ m/s
C) 40 m/s
D) 0.20 km/s
E) 0.40 $\pi$ km/s

Question 52

The graph shows a wave of frequency 3.0 Hz traveling to the right. The phase velocity of this wave is

A) 6 m/s
B) 13 m/s
C) 60 m/s
D) 90 m/s
E) 0.12 km/s

Question 53

Two waveforms of the same frequency are moving to the right. The power P_A transmitted by wave A is equal to

A) 2P_B/3
B) 9P_B/4
C) P_B
D) 4P_B/9
E) P_B

Question 54

A wave moving in the positive x direction has an amplitude of 0.4 m, a frequency of 0.25 Hz, and a wavelength of 24 m. An equation, in which the units are SI, that might describe this wave is

A) y(x, t) = 0.2 sin 2 $\pi$ (t/4 + x/24)
B) y(x, t) = 0.4 sin 2 $\pi$ (t/4 - x/24)
C) y(x, t) = 0.4 sin 8 $\pi$ (t - x/6)
D) y(x, t) = 0.2 sin 0.5 $\pi$ (t/4 - x/24)
E) y(x, t) = 0.4 sin 2 $\pi$ (t/4 + x/6)

Question 55

The power transmitted by any harmonic wave varies directly as

A) the period.
B) the square root of the frequency.
C) the amplitude.
D) the amplitude squared.
E) None of these is correct.

Question 56

The equation that gives the particle displacement of a medium in which there is a simple harmonic progressive wave is
Y(x, t) = (2/ $\pi$ ) sin $\pi$ (x - 4t),
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/ $\pi$ m/s
D) 4 m/s
E) 8 m/s

Question 57

A sinusoidal wave train is moving along a string. The equation giving the displacement y of a point at coordinate x has the form
Y(x, t) = 0.15 sin[10 $\pi$ (t - x/60)]
Where the units are SI. The wavelength is

A) 8.0 cm
B) 15 cm
C) 6.0 m
D) 12 m
E) 60 m

Question 58

To double the rate at which energy is transmitted along a string, you could

A) double the angular frequency of the source.
B) double the amplitude of the wave.
C) double the tension in the string.
D) quadruple the tension in the string.
E) halve the linear density of the string.

Question 59

The particle displacement in a simple harmonic wave is given by
y(x, t) = 2 sin 4 $\pi$ (t + x/8),
Where the units are SI. A graph of particle displacement as a function of position at
T = 0.5s would include points

A) A and D
B) B and D
C) C and E
D) B and E
E) D and F

Question 60

The graph shows a wave moving from left to right. If the period of this wave motion is 50 ms, the wave is moving with a velocity of

A) 40 $\pi$ cm/s
B) 1.6 $\pi$ m/s
C) 1.6 m/s
D) 80 cm/s
E) 0.40 cm/s

Question 61

Waves of amplitude 1.3 cm move along a 14-m long string that has a mass of 90 g and is under a tension of 18 N. If the average total energy of the waves in the string is 5 J, calculate the frequency of the waves.

A) 21 Hz
B) 811 Hz
C) 129 Hz
D) 92 Hz
E) 256 Hz

Question 62

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

A) twenty; twenty
B) one hundred; twenty
C) twenty; four
D) one hundred; four
E) two; two

Question 63

Two sounds differ by 30 dB. The intensity of the louder sound I_L, compared with the softer I_S, is I_L/I_S. The value of the ratio is

A) 1000
B) 30
C) 9
D) 100
E) 300

Question 64

If a sound of intensity I = 1.0 $\times$ 10^-6 W/m² falls on a detector of area A = 7.0 $\times$ 10^-5 m² (about the size of your eardrum), how much power is received by the detector?

A) 6.2 $\times$ 10^-14 W
B) 1.0 $\times$ 10^-6 W
C) 7.0 $\times$ 10^-11 W
D) 1.4 $\times$ 10^-2 W
E) 70 W

Question 65

The intensity of a wave at a certain point is I. A second wave has twice the energy density and three times the speed of the first. What is the intensity of the second wave?

A) I
B) 2I
C) 3I
D) 6I
E) 2I/3

Question 66

If you were to double the speed of a wave on a string while keeping the frequency and amplitude of the wave constant, the rate at which energy is delivered by the wave would

A) double.
B) quadruple.
C) be reduced 50%.
D) be reduced to 25% of its previous value.
E) be unchanged.

Question 67

If you were to quadruple the speed of a wave on a string while keeping the frequency and amplitude of the wave constant, the rate at which energy is delivered by the wave would

A) double.
B) quadruple.
C) be reduced 50%.
D) be reduced to 25% of its previous value.
E) be unchanged.

Question 68

A musical pitch is played at 60 dB. Another is played that sounds four times as loud. The sound intensity level of the second pitch is

A) 80 dB
B) 100 dB
C) 66 dB
D) 64 dB
E) 240 dB

Question 69

You have a rope that is 10 m long and has a mass of 0.2 kg. In addition, you have an oscillator that can generate a 5 Hz wave with an amplitude of 10 cm. What should the tension in the rope be if you need to transmit 10 W of power along the rope?

A) 102 N
B) 205 N
C) 320 N
D) 51 N
E) 250 N

Question 70

The human ear can be sensitive to sound frequencies up to 20 kHz. What wavelength does this correspond to at normal temperature and pressure?

A) 0.165 m
B) 165 cm
C) 16.5 mm
D) 1650 $\times$ 10^-4 m
E) 1.65 mm

Question 71

If you were to reduce the amplitude of a wave on a string by half while keeping the speed and frequency of the wave constant, the energy delivered by the wave would

A) double.
B) quadruple.
C) be reduced 50%.
D) be reduced to 25% of its previous value.
E) be unchanged.

Question 72

Electromagnetic waves

A) include light, radio waves, X rays, gamma rays, and microwaves.
B) do not require a medium for propagation.
C) travel through a vacuum with a speed of approximately 3 $\times$ 10⁸ m/s.
D) are produced when free electrons accelerate.
E) are described by all of the above

Question 73

The sound level of a dog's bark is 50 dB. The intensity of a rock concert is 10,000 times that of the dog's bark. What is the sound level of the rock concert?

A) 10,050 dB
B) 500,000 dB
C) 90 dB
D) 2000 dB
E) 54 dB

Question 74

If you were to reduce the frequency of a wave on a string by a factor of 2 while keeping the speed and amplitude of the wave constant, the rate at which energy is delivered by the wave would

A) double.
B) quadruple.
C) be reduced 50%.
D) be reduced to 25% of its previous value.
E) be unchanged.

Question 75

If you were to double the amplitude and halve the frequency of a wave on a string while keeping the amplitude of the wave constant, the rate at which energy is delivered by the wave would

A) double.
B) quadruple.
C) be reduced 50%.
D) be reduced to 25% of its previous value.
E) be unchanged.

Question 76

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

Question 77

If you were to double the frequency of a wave on a string while keeping the speed and amplitude of the wave constant, the energy delivered by the wave would

A) double.
B) quadruple.
C) be reduced 50%.
D) be reduced to 25% of its previous value.
E) be unchanged.

Question 78

If you were to double the amplitude of a wave on a string while keeping the speed and frequency of the wave constant, the energy delivered by the wave would

A) double.
B) quadruple.
C) be reduced 50%.
D) be reduced to 25% of its previous value.
E) be unchanged.

Question 79

A wave of frequency f is transmitted on a string with tension T. If the tension is increased by a factor of 4 and the frequency and amplitude are unchanged, the power transmitted changed by

A) 1/2
B) 1/4
C) 2
D) 4
E) 1

Question 80

The intensity of a certain spherical wave is 8.0 W/m² at a distance of 1.0 m from the source. If the medium is isotropic and nonabsorbing, the intensity 100 m from the source is

A) 8.0 W/m²
B) 6.4 $\times$ 10^-4 W/m²
C) 1.9 $\times$ 10^-4 W/m²
D) 8.0 $\times$ 10^-4 W/m²
E) 1.9 $\times$ 10^-6 W/m²