Question 1

The diagram shows three identical strings that have been put under tension by suspending masses of 5 kg each. For which is the wave speed the greatest?

Accepted Answer

A)  1 
B)  2 
C)  3 
D)  1 and 3 tie 
E)  2 and 3 tie 
A)  1 
B)  2 
C)  3 
D)  1 and 3 tie 
E)  2 and 3 tie D

Question 2

Suppose the maximum speed of a string carrying a sinusoidal wave is vs. When the displacement of a point on the string is half its maximum, the speed of the point is:

Accepted Answer

A)  vs/2 
B)  2vs 
C)  vs/4 
D)  3vs/4 
E)    
A)  vs/2 
B)  2vs 
C)  vs/4 
D)  3vs/4 
E)    E

Question 3

Let f be the frequency, v the speed, and T the period of a sinusoidal traveling wave. The angular frequency is given by:

Accepted Answer

A)  1/T 
B)  2 $\pi$/T 
C)  vT 
D)  f/T 
E)  T/f 
A)  1/T 
B)  2 $\pi$/T 
C)  vT 
D)  f/T 
E)  T/f B

Question 4

A traveling sinusoidal wave is shown below. At which point is the motion 180$\degree$ out of phase with the motion at point P?

Accepted Answer

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

Question 5

The transverse wave shown is traveling from left to right in a medium. The direction of the instantaneous velocity of the medium at point P is:

Accepted Answer

A)  $\uparrow$ 
B)  $\downarrow$ 
C)  $\rightarrow$ 
D)    
E)  no direction since v = 0 
A)  $\uparrow$ 
B)  $\downarrow$ 
C)  $\rightarrow$ 
D)    
E)  no direction since v = 0

Question 6

A long string is constructed by joining the ends of two shorter strings. The tension in the strings is the same but string I has 4 times the linear mass density of string II. When a sinusoidal wave passes from string I to string II:

Accepted Answer

A)  the frequency decreases by a factor of 4 
B)  the frequency decreases by a factor of 2 
C)  the wavelength decreases by a factor of 4 
D)  the wavelength decreases by a factor of 2 
E)  the wavelength increases by a factor of 2 
A)  the frequency decreases by a factor of 4 
B)  the frequency decreases by a factor of 2 
C)  the wavelength decreases by a factor of 4 
D)  the wavelength decreases by a factor of 2 
E)  the wavelength increases by a factor of 2

Question 7

A transverse traveling sinusoidal wave on a string has a frequency of 100 Hz, a wavelength of 0.040 m and an amplitude of 2.0 mm. The maximum velocity in m/s of any point on the string is:

Accepted Answer

A)  0.2 
B)  1.3 
C)  4 
D)  15 
E)  25 
A)  0.2 
B)  1.3 
C)  4 
D)  15 
E)  25

Question 8

A sinusoidal wave is traveling toward the right as shown. Which letter correctly labels the amplitude of the wave?

Accepted Answer

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

Question 9

Here are the equations for the three waves traveling on separate strings. Rank them according to the maxium transverse speed, least to greatest.

Accepted Answer

A)  1, 2, 3 
B)  1, 3, 2 
C)  2, 1, 3 
D)  2, 3, 1 
E)  3, 1, 2 
A)  1, 2, 3 
B)  1, 3, 2 
C)  2, 1, 3 
D)  2, 3, 1 
E)  3, 1, 2

Question 10

Two traveling waves y1 = A sin[k(x - vt)] and y2 = A sin[k(x + vt)] are superposed on the same string. The distance between the adjacent nodes is:

Accepted Answer

A)  vt/ $\pi$ 
B)  vt/2 $\pi$ 
C)  $\pi$/2k 
D)   $\pi$/k 
E)  2 $\pi$/k 
A)  vt/ $\pi$ 
B)  vt/2 $\pi$ 
C)  $\pi$/2k 
D)   $\pi$/k 
E)  2 $\pi$/k

Question 11

A string carries a sinusoidal wave with an amplitude of 2.0 cm and a frequency of 100 Hz. The maximum speed of any point on the string is:

Accepted Answer

A)  2.0 m/s 
B)  4.0 m/s 
C)  6.3 m/s 
D)  13 m/s 
E)  unknown (not enough information is given) 
A)  2.0 m/s 
B)  4.0 m/s 
C)  6.3 m/s 
D)  13 m/s 
E)  unknown (not enough information is given)

Question 12

Three separate strings are made of the same material. String 1 has length L and tension  $ \tau $, string 2 has length 2L and tension 2 $ \tau $ and string 3 has length 3L and tension 3 $ \tau $. A pulse is started at one end of each string. If the pulses start at the same time, the order in which they reach the other end is:

Accepted Answer

A)  1, 2, 3 
B)  3, 2, 1 
C)  2, 3, 1 
D)  3, 1, 2 
E)  they all take the same time 
A)  1, 2, 3 
B)  3, 2, 1 
C)  2, 3, 1 
D)  3, 1, 2 
E)  they all take the same time

Question 13

The displacement of a string is given by   The wavelength of the wave is:

Accepted Answer

A)  2 $\pi$k/$ \omega $ 
B)  k/$ \omega $ 
C)  $ \omega $k 
D)  2 $\pi$/k 
E)  k/2 $\pi$ 
A)  2 $\pi$k/$ \omega $ 
B)  k/$ \omega $ 
C)  $ \omega $k 
D)  2 $\pi$/k 
E)  k/2 $\pi$

Question 14

A string of length 100 cm is held fixed at both ends and vibrates in a standing wave pattern. The wavelengths of the constituent traveling waves CANNOT be:

Accepted Answer

A)  400 cm 
B)  200 cm 
C)  100 cm 
D)  66.7 cm 
E)  50 cm 
A)  400 cm 
B)  200 cm 
C)  100 cm 
D)  66.7 cm 
E)  50 cm

Question 15

Two sources, S1 and S2, each emit waves of wavelength $\lambda$ in the same medium. The phase difference between the two waves, at the point P shown, is   The quantity $\varepsilon$ is:

Accepted Answer

A)  the distance S1S2 
B)  the angle S1PS2 
C)   $\pi$/2 
D)  the phase difference between the two sources 
E)  zero for transverse waves,  $\pi$ for longitudinal waves 
A)  the distance S1S2 
B)  the angle S1PS2 
C)   $\pi$/2 
D)  the phase difference between the two sources 
E)  zero for transverse waves,  $\pi$ for longitudinal waves

Question 16

For a given medium, the frequency of a wave is:

Accepted Answer

A)  independent of wavelength 
B)  proportional to wavelength 
C)  inversely proportional to wavelength 
D)  proportional to the amplitude 
E)  inversely proportional to the amplitude 
A)  independent of wavelength 
B)  proportional to wavelength 
C)  inversely proportional to wavelength 
D)  proportional to the amplitude 
E)  inversely proportional to the amplitude

Question 17

A wave on a stretched string is reflected from a fixed end P of the string. The phase difference, at P, between the incident and reflected waves is:

Accepted Answer

A)  zero 
B)   $\pi$ rad 
C)   $\pi$/2 rad 
D)  depends on the velocity of the wave 
E)  depends on the frequency of the wave 
A)  zero 
B)   $\pi$ rad 
C)   $\pi$/2 rad 
D)  depends on the velocity of the wave 
E)  depends on the frequency of the wave

Question 18

The speed of a sinusoidal wave on a string depends on:

Accepted Answer

A)  the frequency of the wave 
B)  the wavelength of the wave 
C)  the length of the string 
D)  the tension in the string 
E)  the amplitude of the wave 
A)  the frequency of the wave 
B)  the wavelength of the wave 
C)  the length of the string 
D)  the tension in the string 
E)  the amplitude of the wave

Question 19

Two sinusoidal waves have the same angular frequency, the same amplitude ym, and travel in the same direction in the same medium. If they differ in phase by 50 $\degree$, the amplitude of the resultant wave is given by

Accepted Answer

A)  0.64 ym 
B)  1.3 ym 
C)  0.91 ym 
D)  1.8ym 
E)  0.35 ym 
A)  0.64 ym 
B)  1.3 ym 
C)  0.91 ym 
D)  1.8ym 
E)  0.35 ym

Question 20

A sinusoidal transverse wave is traveling on a string. Any point on the string:

Accepted Answer

A)  moves in the same direction as the wave 
B)  moves in simple harmonic motion with a different frequency than that of the wave 
C)  moves in simple harmonic motion with the same angular frequency as the wave 
D)  moves in uniform circular motion with a different angular speed than the wave 
E)  moves in uniform circular motion with the same angular speed as the wave 
A)  moves in the same direction as the wave 
B)  moves in simple harmonic motion with a different frequency than that of the wave 
C)  moves in simple harmonic motion with the same angular frequency as the wave 
D)  moves in uniform circular motion with a different angular speed than the wave 
E)  moves in uniform circular motion with the same angular speed as the wave

Exam 16: Waves I

The diagram shows three identical strings that have been put under tension by suspending masses of 5 kg each. For which is the wave speed the greatest?

Suppose the maximum speed of a string carrying a sinusoidal wave is vs. When the displacement of a point on the string is half its maximum, the speed of the point is:

Let f be the frequency, v the speed, and T the period of a sinusoidal traveling wave. The angular frequency is given by:

A traveling sinusoidal wave is shown below. At which point is the motion 180 °\degree° out of phase with the motion at point P?

The transverse wave shown is traveling from left to right in a medium. The direction of the instantaneous velocity of the medium at point P is:

A long string is constructed by joining the ends of two shorter strings. The tension in the strings is the same but string I has 4 times the linear mass density of string II. When a sinusoidal wave passes from string I to string II:

A transverse traveling sinusoidal wave on a string has a frequency of 100 Hz, a wavelength of 0.040 m and an amplitude of 2.0 mm. The maximum velocity in m/s of any point on the string is:

A sinusoidal wave is traveling toward the right as shown. Which letter correctly labels the amplitude of the wave?

Here are the equations for the three waves traveling on separate strings. Rank them according to the maxium transverse speed, least to greatest.

Two traveling waves y1 = A sin[k(x - vt)] and y2 = A sin[k(x + vt)] are superposed on the same string. The distance between the adjacent nodes is:

A string carries a sinusoidal wave with an amplitude of 2.0 cm and a frequency of 100 Hz. The maximum speed of any point on the string is:

The displacement of a string is given by The wavelength of the wave is:

A string of length 100 cm is held fixed at both ends and vibrates in a standing wave pattern. The wavelengths of the constituent traveling waves CANNOT be:

Two sources, S1 and S2, each emit waves of wavelength λ\lambdaλ in the same medium. The phase difference between the two waves, at the point P shown, is The quantity ε\varepsilonε is:

For a given medium, the frequency of a wave is:

A wave on a stretched string is reflected from a fixed end P of the string. The phase difference, at P, between the incident and reflected waves is:

The speed of a sinusoidal wave on a string depends on:

Two sinusoidal waves have the same angular frequency, the same amplitude ym, and travel in the same direction in the same medium. If they differ in phase by 50 °\degree° , the amplitude of the resultant wave is given by

A sinusoidal transverse wave is traveling on a string. Any point on the string:

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Suppose the maximum speed of a string carrying a sinusoidal wave is v_s. When the displacement of a point on the string is half its maximum, the speed of the point is:

A traveling sinusoidal wave is shown below. At which point is the motion 180 $\degree$ out of phase with the motion at point P? $A traveling sinusoidal wave is shown below. At which point is the motion 180 \degree out of phase with the motion at point P?$

Two traveling waves y₁ = A sin[k(x - vt)] and y₂ = A sin[k(x + vt)] are superposed on the same string. The distance between the adjacent nodes is:

Two sinusoidal waves have the same angular frequency, the same amplitude y_m, and travel in the same direction in the same medium. If they differ in phase by 50 $\degree$ , the amplitude of the resultant wave is given by