Deck 13: Waves

Question 1

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.

Answer 1

24 Hz.

Question 2

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.

Answer 2

Waves transmit both energy and momentum.

Question 3

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.

Answer 3

Transverse pressure waves can travel through fluids.

Question 4

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 5

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 6

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

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

Question 7

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. There is a small particle attached to the rope, as shown in the figures. If the width of the figure 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 8

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 9

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

A) 40 π cm/s.
B) 1.6 π m/s.
C) 1.6 m/s.
D) 80 cm/s.
E) 0.40 cm/s.

Question 10

A sinusoidal wave train is moving along a string. The equation giving the displacement y of a point at coordinate x has the form 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 11

The equation of a traveling wave is x, t) = 0.02 cos0.25x - 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 12

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

A) 6 cm/s.
B) 13 cm/s.
C) 60 cm/s.
D) 90 cm/s.
E) 1.2 m/s.

Question 13

A wave is traveling with a speed v along the x axis in the positive direction, as shown in the figure. 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 14

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 15

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 16

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 17

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 18

The equation of a transverse wave is where the units are SI. The velocity of the wave is

A) 0.20 m/s.
B) 8 m/s.
C) 40 m/s.
D) 0.20 km/s.
E) 0.40 km/s.

Question 19

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) yx, t) = 2 sinx/4 - t) m.
B) yx, t) = 2 sin16x - 8t) m.
C) yx, t) = 2 sinx/4 + t) m.
D) yx, t) = 4 sinx/4 - t) m.
E) yx, t) = 4 sin16x - 8t) m.

Question 20

A piece of string is subject to a wave motion. The distance between the peaks formed, at one particular moment, is called the wave's

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

Question 21

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 22

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.

Question 23

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 24

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 25

A string is stretched by a force of 4.0 N. The mass per unit length of the string is 4.0  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  10² m/s.

Question 26

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%.

Question 27

A string exactly 2 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 28

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

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

Question 29

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.

Question 30

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) yx, t) = 0.2 sin 2t/4 + x/24).
B) yx, t) = 0.4 sin 2t/4 - x/24).
C) yx, t) = 0.4 sin 8t - x/6).
D) yx, t) = 0.2 sin 0.5t/4 - x/24).
E) yx, t) = 0.4 sin 2t/4 + x/6).

Question 31

An equation that gives the particle displacement for a medium in which there is a simple harmonic traveling wave is , 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 32

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 33

A string of mass 2.4  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 34

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 35

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 36

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 37

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  10² m/s
B) 3.3  10² m/s
C) 1.0  10³ m/s
D) 33 m/s
E) 52 m/s

Question 38

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 39

A string under tension carries transverse waves traveling at speed v. If the same string is under 4 times the tension, what is the wave speed?

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

Question 40

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 41

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 42

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 waves using harmonic waves.

Question 43

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) bounce off each other and switch directions.
C) pass through one another.
D) continue to carry energy.
E) remain transverse.

Question 44

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.

Question 45

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 46

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 60^o is

A) 0.040 m.
B) 0.12 m.
C) 0.14 m.
D) 0.24 m.
E) 25 m.

Question 47

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

Question 48

Two loudspeakers S₁ and S₂, 3.0 m apart, emit the same single-frequency tone in phase at the speakers. A listener directly in front of speaker S₁ notices that the intensity is a minimum when she is 4.0 m from that speaker see figure). The listener now walks around speaker S₁ 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 S₂ 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 m

Question 49

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 50

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 180^o that occurs on reflection of a wave at a fixed end.
E) ability of waves to go around corners.

Question 51

If two identical waves with a phase difference of 6π 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.

Question 52

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 53

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

Question 54

Two loudspeakers S₁ and S₂, 3.0 m apart, emit the same single-frequency tone in phase at the speakers. A listener L directly in front of speaker S₁ 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 kHz

Question 55

What is the phase difference at any given instant between two points on a wave that 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

Question 56

Two waves with the same frequency and wavelength but with different amplitudes are added. If A₁ = 2A₂ and the waves are 180^o out of phase, then the amplitude of the resultant wave is

A) zero.
B) the same as A₁.
C) the same as A₂.
D) equal to A₁ + A₂.
E) coherent.

Question 57

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.

Question 58

At P₁, the waves from sources S₁ and S₂ 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.

Question 59

If two identical waves with a phase difference of 3π 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.

Question 60

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  10^-4 m
E) 1.65 mm

Question 61

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).

Question 62

A pulse moves in a string toward a free end a ring on a post) as indicated in the sketch. On reflection, the pulse would most nearly be represented by

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

Question 63

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.

Question 64

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.

Question 65

The sources S₁ and S₂ 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) 5.

Question 66

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).

Question 67

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.

Question 68

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

Question 69

From the figure, you can conclude that

A) the wave travels slower in the medium to the left of the interface than in the medium to the right of the interface.
B) the wave travels faster in the medium to the left of the interface than in the medium to the right of the interface.
C) the wave is traveling with the same speed on both sides of the interface.
D) the angle of incidence is equal to the angle of refraction.
E) total internal reflection is not possible for a wave traveling from left to right.

Question 70

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).

Question 71

At P₂ the waves from sources S₁ and S₂ 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.

Question 72

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.

Question 73

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.

Question 74

The pulse shown is moving in the string toward a fixed end at the wall. After reflection at the wall, which figure correctly represents the pulse?

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

Question 75

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).

Question 76

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.

Question 77

One wave moves to the right and a second wave reflected) moves to the left to form a stationary wave. At which points) does the stationary wave have a node?

A) 1
B) 3 and 5
C) 2
D) 4 and 6
E) 2, 4, and 6

Question 78

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.

Question 79

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

Question 80

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.