Question 1

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

Accepted Answer

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

Question 2

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

Accepted Answer

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

Question 3

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

Accepted Answer

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. 
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. D

Question 4

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

Accepted Answer

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. 
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 5

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

Accepted Answer

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

Question 6

In standing waves, the separation between adjacent nodes is

Accepted Answer

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

Question 7

The energy in a wave traveling on a string is

Accepted Answer

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. 
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.

Question 8

Two waves have the same amplitude and speed. Their wavelengths

Accepted Answer

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

Question 9

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

Accepted Answer

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

Question 10

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

Accepted Answer

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

Question 11

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

Accepted Answer

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

Question 12

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

Accepted Answer

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

Question 13

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

Accepted Answer

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

Question 14

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

Accepted Answer

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. 
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 15

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

Accepted Answer

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

Question 16

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

Accepted Answer

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

Question 17

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

Accepted Answer

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

Question 18

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

Accepted Answer

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. 
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 19

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

Accepted Answer

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. 
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 20

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

Accepted Answer

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. 
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.

Exam 16: Waves

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

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

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

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

In standing waves, the separation between adjacent nodes is

The energy in a wave traveling on a string is

Two waves have the same amplitude and speed. Their wavelengths

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

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

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

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

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

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

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

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

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

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

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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 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

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

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 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/v₂is

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