Question 1

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 C

Question 2

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 wave number is:

Accepted Answer

A)  0.10 rad/m 
B)  3 $\pi$ rad/m 
C)  10 rad/m 
D)  10 $\pi$ rad/m 
E)  3.0 rad/m 
A)  0.10 rad/m 
B)  3 $\pi$ rad/m 
C)  10 rad/m 
D)  10 $\pi$ rad/m 
E)  3.0 rad/m E

Question 3

A transverse wave travels on a string of length 1.3 m and diameter 1.1 mm, whose mass is 10 g and which is under a tension of 16 N. What is the linear mass density of the string?

Accepted Answer

A)  7.7 x 10-3 kg/m 
B)  0.13 kg/m 
C)  7.7 kg/m 
D)  46 kg/m 
E)  130 kg/m 
A)  7.7 x 10-3 kg/m 
B)  0.13 kg/m 
C)  7.7 kg/m 
D)  46 kg/m 
E)  130 kg/m A

Question 4

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

Accepted Answer

A)  f = 1/T 
B)  f = v + T 
C)  f = vT 
D)  f = v/T 
E)  f = T/v 
A)  f = 1/T 
B)  f = v + T 
C)  f = vT 
D)  f = v/T 
E)  f = T/v

Question 5

A sinusoidal wave is generated by moving the end of a string up and down periodically. The generator does not supply any power when the end of the string

Accepted Answer

A)  has its least acceleration 
B)  has its greatest displacement 
C)  has half its greatest displacement 
D)  has one fourth its greatest displacement 
E)  has its least displacement 
A)  has its least acceleration 
B)  has its greatest displacement 
C)  has half its greatest displacement 
D)  has one fourth its greatest displacement 
E)  has its least displacement

Question 6

A standing wave pattern is established in a string as shown. The wavelength of one of the component traveling waves is:

Accepted Answer

A)  0.25 m 
B)  0.5 m 
C)  1 m 
D)  2 m 
E)  4 m 
A)  0.25 m 
B)  0.5 m 
C)  1 m 
D)  2 m 
E)  4 m

Question 7

When a string is vibrating in a standing wave pattern the power transmitted across an antinode, compared to the power transmitted across a node, is:

Accepted Answer

A)  more 
B)  less 
C)  the same (zero) 
D)  the same (non-zero) 
E)  sometimes more, sometimes less, and sometimes the same 
A)  more 
B)  less 
C)  the same (zero) 
D)  the same (non-zero) 
E)  sometimes more, sometimes less, and sometimes the same

Question 8

The displacement of an element of a string is given by y(x,t) = 4.3sin(1.2x - 4.7t - π/3), with x in meters and t in seconds. Given that , what is v?

Accepted Answer

A)  0.065 m/s 
B)  0.25 m/s 
C)  2.0 m/s 
D)  3.9 m/s 
E)  15 m/s 
A)  0.065 m/s 
B)  0.25 m/s 
C)  2.0 m/s 
D)  3.9 m/s 
E)  15 m/s

Question 9

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 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 10

In the diagram below, the interval PQ represents:

Accepted Answer

A)  wavelength/2 
B)  wavelength 
C)  2 * amplitude 
D)  period/2 
E)  period 
A)  wavelength/2 
B)  wavelength 
C)  2 * amplitude 
D)  period/2 
E)  period

Question 11

When a certain string is clamped at both ends, the lowest four resonant frequencies are measured to be 100, 150, 200, and 250 Hz. One of the resonant frequencies (below 200 Hz) is missing. What is it?

Accepted Answer

A)  25 Hz 
B)  50 Hz 
C)  75 Hz 
D)  125 Hz 
E)  225 Hz 
A)  25 Hz 
B)  50 Hz 
C)  75 Hz 
D)  125 Hz 
E)  225 Hz

Question 12

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)  0.20 cm 
B)  2.0 cm 
C)  5.0 cm 
D)  20 cm 
E)  400 cm 
A)  0.20 cm 
B)  2.0 cm 
C)  5.0 cm 
D)  20 cm 
E)  400 cm

Question 13

What are the three main types of waves?

Accepted Answer

A)  transverse, longitudinal, linear 
B)  plane, spherical, transverse 
C)  mechanical, electromagnetic, matter 
D)  transverse, linear, water 
E)  plane, longitudinal, mechanical 
A)  transverse, longitudinal, linear 
B)  plane, spherical, transverse 
C)  mechanical, electromagnetic, matter 
D)  transverse, linear, water 
E)  plane, longitudinal, mechanical

Question 14

The displacement of a string carrying a traveling sinusoidal wave is given by   At time t = 0 the point at x = 0 has velocity v0 and displacement y0. The phase constant $\phi$ is given by tan$\phi$ =:

Accepted Answer

A)  v0/$ \omega $y0 
B)  $ \omega $y0/v0 
C)  $ \omega $v0/y0 
D)  y0/$ \omega $v0 
E)  $ \omega $v0y0 
A)  v0/$ \omega $y0 
B)  $ \omega $y0/v0 
C)  $ \omega $v0/y0 
D)  y0/$ \omega $v0 
E)  $ \omega $v0y0

Question 15

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)  67 cm 
E)  50 cm 
A)  400 cm 
B)  200 cm 
C)  100 cm 
D)  67 cm 
E)  50 cm

Question 16

Two waves are traveling on two different strings. The displacement of one is given by y1(x,t) = ymsin(kx + $ \omega $t) and of the other by y2(x,t) = ymsin(kx + $ \omega $t + φ). What is the difference between these two waves?

Accepted Answer

A)  The displacement of wave y1 is always greater than the displacement of wave y2. 
B)  Wave y1 has a smaller amplitude than wave y2. 
C)  Wave y1 has a higher frequency than wave y2. 
D)  Wave y1 has a shorter wavelength than wave y2. 
E)  The two waves are identical except for their displacement at time t = 0. 
A)  The displacement of wave y1 is always greater than the displacement of wave y2. 
B)  Wave y1 has a smaller amplitude than wave y2. 
C)  Wave y1 has a higher frequency than wave y2. 
D)  Wave y1 has a shorter wavelength than wave y2. 
E)  The two waves are identical except for their displacement at time t = 0.

Question 17

The sinusoidal wave y(x,t) = ymsin(kx - $ \omega $t)
Is incident on the fixed end of a string at x = L. The reflected wave is given by:

Accepted Answer

A)  ymsin(kx + $ \omega $t) 
B)  -ymsin(kx + $ \omega $t) 
C)  ymsin(kx +$ \omega $t - kL) 
D)  ymsin(kx + $ \omega $t - 2kL) 
E)  -ymsin(kx + $ \omega $t + 2kL) 
A)  ymsin(kx + $ \omega $t) 
B)  -ymsin(kx + $ \omega $t) 
C)  ymsin(kx +$ \omega $t - kL) 
D)  ymsin(kx + $ \omega $t - 2kL) 
E)  -ymsin(kx + $ \omega $t + 2kL)

Question 18

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 19

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 20

The sum of two sinusoidal traveling waves is a sinusoidal traveling wave only if:

Accepted Answer

A)  their amplitudes are the same and they travel in the same direction 
B)  their amplitudes are the same and they travel in opposite directions 
C)  their frequencies are the same and they travel in the same direction 
D)  their frequencies are the same and they travel in opposite directions 
E)  their frequencies are the same and their amplitudes are the same 
A)  their amplitudes are the same and they travel in the same direction 
B)  their amplitudes are the same and they travel in opposite directions 
C)  their frequencies are the same and they travel in the same direction 
D)  their frequencies are the same and they travel in opposite directions 
E)  their frequencies are the same and their amplitudes are the same

Exam 16: Waves I

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:

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 wave number is:

A transverse wave travels on a string of length 1.3 m and diameter 1.1 mm, whose mass is 10 g and which is under a tension of 16 N. What is the linear mass density of the string?

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

A sinusoidal wave is generated by moving the end of a string up and down periodically. The generator does not supply any power when the end of the string

A standing wave pattern is established in a string as shown. The wavelength of one of the component traveling waves is:

When a string is vibrating in a standing wave pattern the power transmitted across an antinode, compared to the power transmitted across a node, is:

The displacement of an element of a string is given by y(x,t) = 4.3sin(1.2x - 4.7t - π/3), with x in meters and t in seconds. Given that , what is v?

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:

In the diagram below, the interval PQ represents:

When a certain string is clamped at both ends, the lowest four resonant frequencies are measured to be 100, 150, 200, and 250 Hz. One of the resonant frequencies (below 200 Hz) is missing. What is it?

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:

What are the three main types of waves?

The displacement of a string carrying a traveling sinusoidal wave is given by At time t = 0 the point at x = 0 has velocity v0 and displacement y0. The phase constant ϕ\phiϕ is given by tan ϕ\phiϕ =:

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 waves are traveling on two different strings. The displacement of one is given by y1(x,t) = ymsin(kx + ω \omega ω t) and of the other by y2(x,t) = ymsin(kx + ω \omega ω t + φ). What is the difference between these two waves?

The sinusoidal wave y(x,t) = ymsin(kx - ω \omega ω t) Is incident on the fixed end of a string at x = L. The reflected wave 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?

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:

The sum of two sinusoidal traveling waves is a sinusoidal traveling wave only if:

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Two waves are traveling on two different strings. The displacement of one is given by y₁(x,t) = y_msin(kx + $\omega$ t) and of the other by y₂(x,t) = y_msin(kx + $\omega$ t + φ). What is the difference between these two waves?

The sinusoidal wave y(x,t) = y_msin(kx - $\omega$ t) Is incident on the fixed end of a string at x = L. The reflected wave 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? $A traveling sinusoidal wave is shown below. At which point is the motion 180 \degree out of phase with the motion at point P?$