Question 1

A 40-cm long string, with one end clamped and the other free to move transversely, is vibrating in its fundamental standing wave mode. If the wave speed is 320 cm/s the frequency is:

Accepted Answer

A)  32 Hz 
B)  16 Hz 
C)  8 Hz 
D)  4 Hz 
E)  2 Hz 
A)  32 Hz 
B)  16 Hz 
C)  8 Hz 
D)  4 Hz 
E)  2 Hz

Question 2

A 30-cm long string, with one end clamped and the other free to move transversely, is vibrating in its second harmonic. The wavelength of the constituent traveling waves is:

Accepted Answer

A)  10 cm 
B)  30 cm 
C)  40 cm 
D)  60 cm 
E)  120 cm 
A)  10 cm 
B)  30 cm 
C)  40 cm 
D)  60 cm 
E)  120 cm

Question 3

If $\lambda$ is the wavelength of the each of the component sinusoidal traveling waves that form a standing wave, the distance between adjacent nodes in the standing wave is:

Accepted Answer

A)  $\lambda$/4 
B)  $\lambda$/2 
C)  3$\lambda$/4 
D)  $\lambda$ 
E)  2$\lambda$ 
A)  $\lambda$/4 
B)  $\lambda$/2 
C)  3$\lambda$/4 
D)  $\lambda$ 
E)  2$\lambda$

Question 4

When a certain string is clamped at both ends, the lowest four resonant frequencies are 50, 100, 150, and 200 Hz. When the string is also clamped at its midpoint, the lowest four resonant frequencies are:

Accepted Answer

A)  50, 100, 150, and 200 Hz 
B)  50, 150, 250, and 300 Hz 
C)  100, 200, 300, and 400 Hz 
D)  25, 50 75, and 100 Hz 
E)  75, 150, 225, and 300 Hz 
A)  50, 100, 150, and 200 Hz 
B)  50, 150, 250, and 300 Hz 
C)  100, 200, 300, and 400 Hz 
D)  25, 50 75, and 100 Hz 
E)  75, 150, 225, and 300 Hz

Question 5

Which of the following represents a standing wave?

Accepted Answer

A)  y = (6.0 mm)sin[(3.0 m-1)x + (2.0 s-1)t] - (6.0 mm)cos[(3.0 m-1)x + 2.0] 
B)  y = (6.0 mm)cos[(3.0 m-1)x - (2.0 s-1)t] + (6.0 mm)cos[(2.0 s-1)t + 3.0 m-1)x] 
C)  y = (6.0 mm)cos[(3.0 m-1)x - (2.0 s-1)t] - (6.0 mm)sin[(2.0 s-1)t - 3.0] 
D)  y = (6.0 mm)sin[(3.0 m-1)x - (2.0 s-1)t] - (6.0 mm)cos[(2.0 s-1)t + 3.0 m-1)x] 
E)  y = (6.0 mm)sin[(3.0 m-1)x] + (6.0 mm)cos[(2.0 s-1)t] 
A)  y = (6.0 mm)sin[(3.0 m-1)x + (2.0 s-1)t] - (6.0 mm)cos[(3.0 m-1)x + 2.0] 
B)  y = (6.0 mm)cos[(3.0 m-1)x - (2.0 s-1)t] + (6.0 mm)cos[(2.0 s-1)t + 3.0 m-1)x] 
C)  y = (6.0 mm)cos[(3.0 m-1)x - (2.0 s-1)t] - (6.0 mm)sin[(2.0 s-1)t - 3.0] 
D)  y = (6.0 mm)sin[(3.0 m-1)x - (2.0 s-1)t] - (6.0 mm)cos[(2.0 s-1)t + 3.0 m-1)x] 
E)  y = (6.0 mm)sin[(3.0 m-1)x] + (6.0 mm)cos[(2.0 s-1)t]

Question 6

A 40-cm long string, with one end clamped and the other free to move transversely, is vibrating in its fundamental standing wave mode. The wavelength of the constituent traveling waves is:

Accepted Answer

A)  10 cm 
B)  20 cm 
C)  40 cm 
D)  80 cm 
E)  160 cm 
A)  10 cm 
B)  20 cm 
C)  40 cm 
D)  80 cm 
E)  160 cm

Question 7

Three traveling sinusoidal waves are on identical strings, with the same tension. The mathematical forms of the waves are y1(x,t) = ymsin(3x - 6t), y2(x,t) = ymsin(4x - 8t), and y3(x,t) = ymsin(6x - 12t), where x is in meters and t is in seconds. Match each mathematical form to the appropriate graph below.

Accepted Answer

A)  y1: i, y2: ii, y3: iii 
B)  y1: iii, y2: ii, y3: i 
C)  y1:i, y2: iii, y3: ii 
D)  y1: ii, y2: i, y3: iii 
E)  y1: iii, y2: i, y3: ii 
A)  y1: i, y2: ii, y3: iii 
B)  y1: iii, y2: ii, y3: i 
C)  y1:i, y2: iii, y3: ii 
D)  y1: ii, y2: i, y3: iii 
E)  y1: iii, y2: i, y3: ii

Question 8

A long string is constructed by joining the ends of 2 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 wave speed decreases by a factor of 4 
D)  the wave speed decreases by a factor of 2 
E)  the wave speed 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 wave speed decreases by a factor of 4 
D)  the wave speed decreases by a factor of 2 
E)  the wave speed increases by a factor of 2

Question 9

The tension in a string with a linear density of 0.0010 kg/m is 0.40 N. A 100 Hz sinusoidal wave on this string has a wavelength of:

Accepted Answer

A)  0.05 cm 
B)  2.0 cm 
C)  5.0 cm 
D)  20 cm 
E)  100 cm 
A)  0.05 cm 
B)  2.0 cm 
C)  5.0 cm 
D)  20 cm 
E)  100 cm

Question 10

A wave is described by y(x,t) = 0.1 sin(3x - 10t), where x is in meters, y is in centimeters and t is in seconds. The angular frequency is:

Accepted Answer

A)  0.10 rad/s 
B)  3.0 rad/s 
C)  10 $\pi$ rad/s 
D)  20 $\pi$ rad/s 
E)  (10/ rad/s 
A)  0.10 rad/s 
B)  3.0 rad/s 
C)  10 $\pi$ rad/s 
D)  20 $\pi$ rad/s 
E)  (10/ rad/s

Question 11

Fully destructive interference between two sinusoidal waves of the same frequency and amplitude occurs only if they:

Accepted Answer

A)  travel in opposite directions and are in phase 
B)  travel in opposite directions and are 180 $\degree$out of phase 
C)  travel in the same direction and are in phase 
D)  travel in the same direction and are 180 $\degree$out of phase 
E)  travel in the same direction and are 90 $\degree$ out of phase 
A)  travel in opposite directions and are in phase 
B)  travel in opposite directions and are 180 $\degree$out of phase 
C)  travel in the same direction and are in phase 
D)  travel in the same direction and are 180 $\degree$out of phase 
E)  travel in the same direction and are 90 $\degree$ out of phase

Exam 16: Waves I

A 40-cm long string, with one end clamped and the other free to move transversely, is vibrating in its fundamental standing wave mode. If the wave speed is 320 cm/s the frequency is:

A 30-cm long string, with one end clamped and the other free to move transversely, is vibrating in its second harmonic. The wavelength of the constituent traveling waves is:

If λ\lambdaλ is the wavelength of the each of the component sinusoidal traveling waves that form a standing wave, the distance between adjacent nodes in the standing wave is:

When a certain string is clamped at both ends, the lowest four resonant frequencies are 50, 100, 150, and 200 Hz. When the string is also clamped at its midpoint, the lowest four resonant frequencies are:

Which of the following represents a standing wave?

A 40-cm long string, with one end clamped and the other free to move transversely, is vibrating in its fundamental standing wave mode. The wavelength of the constituent traveling waves is:

A long string is constructed by joining the ends of 2 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:

The tension in a string with a linear density of 0.0010 kg/m is 0.40 N. A 100 Hz sinusoidal wave on this string has a wavelength of:

A wave is described by y(x,t) = 0.1 sin(3x - 10t), where x is in meters, y is in centimeters and t is in seconds. The angular frequency is:

Fully destructive interference between two sinusoidal waves of the same frequency and amplitude occurs only if they:

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If $\lambda$ is the wavelength of the each of the component sinusoidal traveling waves that form a standing wave, the distance between adjacent nodes in the standing wave is: