Deck 16: Waves

Question 1

The energy in a wave traveling on a string is

A) distributed roughly uniformly throughout the length of the string.
B) concentrated at the crests and troughs.
C) concentrated where the slope of the string is at a maximum.
D) zero because no part of the string travels from one point in space to another.
E) zero because no energy is distributed anywhere along a string wave.

Answer 1

concentrated where the slope of the string is at a maximum.

Question 2

In a "dispersive" medium, waves exhibit all of the following features except that

A) a wave pulse tends to change shape as it propagates.
B) waves move at a speed that is dependent on wavelength.
C) the phase velocity differs from the group velocity.
D) none of the first three statements is correct.
E) all of the first three statements are correct.

Answer 2

all of the first three statements are correct.

Question 3

A transverse wave travels from left to right along a perfectly elastic string parallel with the ground. Any given point on the string is

A) moving up and down.
B) moving up only.
C) moving down only.
D) moving left and right.
E) fixed in place; it does not move at all.

Answer 3

moving up and down.

Question 4

A transverse wave travels from left to right along a perfectly elastic string parallel with the ground. The velocity of any given point on the string is

A) pointing in the same direction as the velocity of the wave.
B) pointing in the direction opposite that of the velocity of the wave.
C) zero.
D) perpendicular to the velocity of the wave.
E) the same as the velocity of the wave.

Question 5

A longitudinal wave travels from left to right along a perfectly elastic string parallel with the ground. Any given point on the string is

A) moving up and down.
B) moving right only.
C) moving down only.
D) moving left and right.
E) fixed in place; it does not move at all.

Question 6

Two waves have the same amplitude and speed. Their wavelengths

A) are the same.
B) are different.
C) are unknown; more information is needed to work out the answer.

Question 7

The number of crests of a wave passing a point per unit time is the wave's

A) amplitude.
B) period.
C) frequency.
D) velocity.
E) phase angle.

Question 8

The points separated by a wavelength in the following wave pattern (photograph taken at a certain instant in timeare

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

Question 9

In which of the following media will a wave propagate at the largest speed?

A) A loose, light rope.
B) A loose, heavy rope.
C) A tight, light rope.
D) A tight, heavy rope.

Question 10

A person with her ear to the ground sees a huge stone strike some concrete pavement. A while later she hears two sounds from the impact: One travels in air and the other in concrete, and they are 1.1 s apart. The speed of sound in air is 343 m/s and in concrete is 3000 m/s. The distance from the point of impact is

A) 0.33 km.
B) 0.34 km.
C) 0.38 km.
D) 0.43 km.
E) 0.68 km.

Question 11

Two strings, one thick and the other thin, are connected to form one long string. As a wave travels along the string and passes the point where the two strings are connected, all of the following change except for the

A) frequency of the wave.
B) speed of the wave.
C) wavelength of the wave.
D) wave number of the wave.

Question 12

Two strings, one thick (linear density 2 $\mu$ ) and the other thin (linear density $\mu$ ), are connected to form one long string. The speed of a wave traveling along the string and from the larger-linear density to the lower-linear density parts is

A) unchanged.
B) decreased by a factor of 2.
C) increased by a factor of 2.
D) decreased by a factor of $\sqrt { 2 }$
E) increased by a factor of $\sqrt { 2 }$

Question 13

A tidal wave (tsunami) of wavelength 4.8 $\times$ 10⁵ m travels at 200 m/s in the open ocean. The time between two successive incoming waves is

A) 0.21 $\times$ 10^-3 s.
B) 0.42 $\times$ 10^-3 s.
C) 24 s.
D) 20 minutes.
E) 40 minutes.

Question 14

A wave is given by the equation $y ( x , t ) = 4.0 \cos ( 6 \pi x - 10 \pi t )$ m. The frequency of the wave is

A) 3 Hz.
B) 5 Hz.
C) 5/3 Hz.
D) 1/5 Hz.
E) 1/3 Hz.

Question 15

When the amplitude of a wave is tripled, its frequency will

A) decrease by a factor of 4.
B) decrease by a factor of 2.
C) stay the same.
D) increase by a factor of 2.
E) increase by a factor of 4.

Question 16

A wave is given by the equation $y ( x , t ) = 4.0 \cos ( 6 \pi x - 10 \pi t )$ m. The speed of the wave is

A) 20 m/s.
B) 15 m/s.
C) 12 m/s.
D) 3/5 m/s.
E) 5/3 m/s.

Question 17

The speed of sound in biological tissue is 1500 m/s. To resolve features with sizes of the order of two millimeters, the frequency of the sound wave used by a doctor is

A) larger than 3.0 $\times$ 10⁵ Hz.
B) smaller than 3.0 $\times$ 10⁵ Hz.
C) 7.5 $\times$ 10⁵ Hz.
D) larger than 7.5 $\times$ 10⁵ Hz.
E) smaller than 7.5 $\times$ 10⁵ Hz.

Question 18

A wave is represented by $y ( x , t ) = - A \cos ( \omega t - k x )$ . The direction the wave moves in is

A) the positive x direction.
B) the negative x direction.
C) the positive y direction.
D) the negative y direction.
E) none of the above.

Question 19

A string is composed of two parts, each made of the same material and one having four times the diameter of the other. The string, subject to a tension T, is plucked so that a pulse moves along it at speed v₁ in the thick part and at speed v₂ in the thin part. The ratio of v₁/v₂ is

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

Question 20

Cold spots in a microwave oven are found to be 1.25 cm apart. The frequency of the microwaves used is

A) 24.0 GHz.
B) 12.0 GHz.
C) 54.9 kHz.
D) 27.4 kHz.
E) 3.64 mHz.

Question 21

The phase difference between a crest of a wave and the adjacent trough is

A) 2 $\pi$ rad.
B) $\pi$ rad.
C) $\pi$ /2 rad.
D) $\pi$ /4 rad.
E) 0 rad.

Question 22

A wave traveling on a string is described by the expression $y ( x , t ) = 5.0 \cos \left( \frac { \pi } { 3 } x + \frac { \pi } { 6 } t - \frac { 3 \pi } { 2 } \right)$ cm where $x$ is measured in meters and $t$ in seconds. The phase difference at the same point on the string over a time difference of 3.0 s is

A) $\pi$ /6 rad.
B) $\pi$ /3 rad.
C) $\pi$ /2 rad.
D) $\pi$ rad.
E) 2 $\pi$ rad.

Question 23

A wave traveling on a string is described by the expression $y ( x , t ) = 5.0 \cos \left( \frac { \pi } { 3 } x + \frac { \pi } { 6 } t - \frac { 3 \pi } { 2 } \right)$ cm where $x$ is measured in meters and $t$ in seconds. The phase difference at the same moment in time between two points on the string 25.0 cm apart is

A) $\pi$ /12 rad.
B) $\pi$ /4 rad.
C) $\pi$ /3 rad.
D) $\pi$ rad.
E) 2 $\pi$ rad.

Question 24

A student studies the motion of a transverse wave moving along a stretched string in the negative $x$ direction. At time $t = 1.0 \mathrm {~s}$ the student takes a photograph of the wave, and she is able to establish that the amplitude of the wave is $10.0 \mathrm {~cm}$ , the wavelength is $3.0 \mathrm {~m}$ , and the piece of string at position $x = 3.0 \mathrm {~m}$ is displaced from its equilibrium position by $- 10.0 \mathrm {~cm}$ . When studying the time behavior of this piece of the string at position $x = 3.0 \mathrm {~m}$ , she finds that it oscillates up and down with a frequency of $0.25 \mathrm {~Hz}$ . Based on these observations, the precise equation describing the wave is

A) $y ( x , t ) = 10 \cos [ 2 \pi ( x / 3 - t / 4 + 1 / 4 ) ]$ cm.
B) $y ( x , t ) = 10 \cos [ 2 \pi ( x / 3 + t / 4 + 1 / 4 ) ]$ cm.
C) $y ( x , t ) = 10 \cos [ 2 \pi ( x / 3 - t / 4 - 1 / 4 ) ]$ cm.
D) $y ( x , t ) = 10 \cos ( 2 \pi x / 3 + t / 4 + 1 / 4 )$ cm.
E) $y ( x , t ) = 10 \cos 2 \pi ( x / 3 ) - t / 4 + 1 / 4$ cm.

Question 25

A 100-Hz sound wave travels with a speed of 343 m/s. The distance between two points whose phase differs by $\pi$ /2 at the same moment is

A) 6.86 m.
B) 3.43 m.
C) 1.72 m.
D) 85.8 cm.
E) 42.9 cm.

Question 26

All of the following are solutions to the wave equation except for

A) $y ( x , t ) = A \cos [ k ( x - v t ) ]$
B) $y ( x , t ) = A \cos ( k x - a t )$
C) $y ( x , t ) = A \cos [ 2 \pi ( x / \lambda - f ) ]$
D) all of the first three are correct.
E) none of the first three is correct.

Question 27

A pulse is traveling in a taut string from left to right. The shape of the pulse reflected at the fixed end of the string is

A) A
B) B
C) C
D) D

Question 28

A pulse is traveling in a taut string from left to right. The shape of the pulse reflected at the free end of the string is

A) A
B) B
C) C
D) D

Question 29

Two pulses are moving on a taut string toward each other at 3.0 m/s. The graph that best describes the position of the two pulses 2.0 s later is

A) A
B) B
C) C
D) D
E) E

Question 30

When destructive interference occurs, the resultant disturbance of the medium (compared to its value if there is no such destructive interference) is

A) reduced.
B) unchanged.
C) increased.

Question 31

Two waves with the same frequency and wavelength but the amplitudes A₂ = 3A₁ are $\pi$ rad out of phase. The amplitude of the resultant wave is

A) zero.
B) A₁.
C) 2A₁.
D) 3A₁.
E) 4A₁.

Question 32

Two waves with the same frequency and wavelength but the amplitudes A₂ = 3A₁ are 4 $\pi$ rad out of phase. The amplitude of the resultant wave is

A) zero.
B) A₁.
C) 2A₁.
D) 3A₁.
E) 4A₁.

Question 33

The curve on the right side graph that represents the wave resulting from the superposition of the two waves in the left side graph is

A) A
B) B
C) C
D) D

Question 34

Two loudspeakers 6.00 m apart emit the same frequency tone in phase at the speakers. A listener notices that the intensity of the sound is minimized when she is placed 8.00 m in front of the second speaker. The lowest frequency of the emitted tone (assume the speed of sound in air is 343 m/s) is

A) 1.03 kHz.
B) 686 Hz.
C) 343 Hz.
D) 172 Hz.
E) 85.8 Hz.

Question 35

Two loudspeakers 6.00 m apart emit the same frequency tone in phase at the speakers. A listener notices that the intensity of the sound is minimized when she is placed at A, 8.00 m in front of the second speaker. The listener starts walking toward the first speaker in a circle of radius 8.00 m until she reaches B, where she hears the first maximum. Assuming the speed of sound in air is 343 m/s, the length of the arc AB is

A) 12.3 m.
B) 9.23 m.
C) 6.15 m.
D) 3.08 m.
E) 1.58 m.

Question 36

In standing waves, the separation between adjacent nodes is

A) $\lambda$ /4.
B) $\lambda$ /2.
C) $\lambda$
D) 2 $\lambda$
E) 4 $\lambda$

Question 37

The tension in a violin string is tripled. As a result, the frequency of the first overtone of that string will increase by a factor of

A) 0.33
B) 0.59.
C) 1.7.
D) 3.0.
E) 9.0.

Question 38

One end of a horizontal string of 0.40 mg/m mass per unit length is attached to a small-amplitude mechanical 60 Hz vibrator. The string passes over a pulley, a distance L = 2.5 m away, and weights are hung from this end. Assume the string at the vibrator is a node, which is nearly true. The mass that must be hung from the end of the string to produce three loops of a standing wave is

A) 800 g.
B) 400 g.
C) 100 g.
D) 40 g.
E) 10 g.

Question 39

For a standing wave, the medium is at rest

A) everywhere, at certain times.
B) all the time, at certain positions.
C) everywhere, all the time.
D) nowhere, at no time.

Question 40

A guitar string is 0.73 m long and is tuned to play E above middle C (330 Hz). To play A above middle C (440 Hz), the position of the player's finger measured from the end of the string is

A) 0.18 m.
B) 0.24 m
C) 0.32 m.
D) 0.41 m.
E) 0.50 m.

Question 41

For standing waves, the only wave characteristic independent of the specific wave mode is the

A) frequency of the wave.
B) wavelength of the wave.
C) speed of the wave.
D) period of the wave.

Question 42

When vibrating at a frequency of 12 Hz, a standing wave pattern containing four loops is produced in a string fixed at both ends. To produce a standing wave pattern containing five loops, the frequency of vibration is

A) 1.7 Hz.
B) 4.0 Hz.
C) 9.6 Hz.
D) 15 Hz.
E) 60 Hz.

Question 43

A finger is placed at a point one-third of the distance from one end to the other of a 2.0-m taut string. The speed at which waves move along the string is 400 m/s. When the string is lightly plucked, the lowest frequency produced is

A) 33 Hz.
B) 50 Hz.
C) 100 Hz.
D) 200 Hz.
E) 300 Hz.

Question 44

The wave equation for a standing wave on a string fixed at both ends is $y ( x , t ) = 24 \cos ( 3.0 x ) \cos ( 2 t )$ cm. The distance between two successive nodes on the string is

A) 1.0 cm.
B) 2.1 cm.
C) 1.5 m.
D) 1.0 m.
E) 2.1 m.

Question 45

The wave equation for a standing wave on a string fixed at both ends is $y ( x , t ) = 24 \cos ( 3.0 x ) \cos ( 2 t )$ cm. The speed of the traveling waves that result in this standing wave is

A) 0.67 m/s.
B) 1.5 m/s.
C) 8.0 m/s.
D) 1.5 cm/s.
E) 0.67 cm/s.

Question 46

The human ear canal is approximately 2.50 cm long. It is open to the outside and is closed at the other end by the eardrum. All of the following are frequencies (in the audible range of 20 Hz - 20 kHz) of the standing waves in the ear canal except for

A) 3430 Hz.
B) 13,700 Hz.
C) 10,300 Hz.
D) 17,200 Hz.

Question 47

Two guitar players are simultaneously playing a note. One note is played at 420 Hz; the other is played at 424 Hz. The resulting tone will be at

A) 844 Hz with a beat frequency at 4 Hz.
B) 422 Hz with a beat frequency at 2 Hz.
C) 422 Hz with a beat frequency at 4 Hz.
D) 2 Hz with a beat frequency at 422 Hz.
E) 4 Hz with a beat frequency at 422 Hz.

Question 48

A pianist is playing a 30.87-Hz and a 32.70-Hz note. The beat heard is

A) 63.57 Hz.
B) 31.78 Hz.
C) 1.83 Hz.
D) 0.91 Hz.

Question 49

The beat frequency heard when two notes are played is 4 Hz. If one of the notes played was 53 Hz, the other note was

A) 57 Hz.
B) 55 Hz.
C) 51 Hz.
D) 49 Hz or 57 Hz.
E) 51 Hz or 55 Hz.

Question 50

The change described by the beat frequency is in

A) velocity.
B) wavelength.
C) pitch.
D) intensity.
E) frequency.

Question 51

The graphs here show beats that occur when two different pairs of waves are added. The pair of original waves with the highest frequency difference is

A) shown in the top graph.
B) shown in the bottom graph.
C) shown in either one of the two graphs because they correspond to the same frequency difference.
D) shown in either one of the two graphs because they correspond to the same amplitude difference.
E) unknown; more information is needed to work out the answer.