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

The time required for a small pulse to travel from A to B on a stretched cord shown is NOT altered by changing:

Accepted Answer

A) the linear mass density of the cord 
B) the length between A and B 
C) the shape of the pulse 
D) the tension in the cord 
E) none of the above (changes in all alter the time) 
A) the linear mass density of the cord 
B) the length between A and B 
C) the shape of the pulse 
D) the tension in the cord 
E) none of the above (changes in all alter the time) C

Question 3

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" D

Question 4

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 5

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 6

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 7

Two traveling sinusoidal waves interfere to produce a wave with the mathematical form   If the value of $\phi$is appropriately chosen, the two waves might be:

Accepted Answer

A) y1(x,t)= (ym/3)sin (kx +  $ \omega $t)and y2(x,t)= (ym/3)sin (kx +  $ \omega $t + $\phi$) 
B) y1(x,t)= 0.7ym sin (kx -  $ \omega $t)and y2(x,t)= 0.7ym sin (kx -  $ \omega $t + $\phi$) 
C) y1(x,t)= 0.7ym sin (kx -  $ \omega $t)and y2(x,t)= 0.7ym sin (kx +  $ \omega $t + $\phi$) 
D) y1(x,t)= 0.7ym sin [(kx/2)- ( $ \omega $t/2)] and y2(x,t)= 0.7ym sin [(kx/2)- ( $ \omega $t/2)+ $\phi$] 
E) y1(x,t)= 0.7ym sin (kx +  $ \omega $t)and y2(x,t)= 0.7ym sin (kx +  $ \omega $t + $\phi$) 
A) y1(x,t)= (ym/3)sin (kx +  $ \omega $t)and y2(x,t)= (ym/3)sin (kx +  $ \omega $t + $\phi$) 
B) y1(x,t)= 0.7ym sin (kx -  $ \omega $t)and y2(x,t)= 0.7ym sin (kx -  $ \omega $t + $\phi$) 
C) y1(x,t)= 0.7ym sin (kx -  $ \omega $t)and y2(x,t)= 0.7ym sin (kx +  $ \omega $t + $\phi$) 
D) y1(x,t)= 0.7ym sin [(kx/2)- ( $ \omega $t/2)] and y2(x,t)= 0.7ym sin [(kx/2)- ( $ \omega $t/2)+ $\phi$] 
E) y1(x,t)= 0.7ym sin (kx +  $ \omega $t)and y2(x,t)= 0.7ym sin (kx +  $ \omega $t + $\phi$)

Question 8

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 9

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 10

Fully constructive interference between two sinusoidal waves of the same frequency occurs only if they:

Accepted Answer

A) travel in the same direction and are 270  $\degree$out of phase 
B) travel in the same direction and are 45  $\degree$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 the same direction and are 270  $\degree$out of phase 
B) travel in the same direction and are 45  $\degree$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

Question 11

What is the difference between transverse and longitudinal waves?

Accepted Answer

A) Mechanical waves are transverse waves while electromagnetic waves are longitudinal. 
B) Plane waves are transverse waves while spherical waves are longitudinal. 
C) Only longitudinal waves transmit matter. 
D) Only transverse waves transmit energy. 
E) In transverse waves the displacement is perpendicular to the direction of propagation of the wave, while in longitudinal waves the displacement is parallel to the direction of propagation. 
A) Mechanical waves are transverse waves while electromagnetic waves are longitudinal. 
B) Plane waves are transverse waves while spherical waves are longitudinal. 
C) Only longitudinal waves transmit matter. 
D) Only transverse waves transmit energy. 
E) In transverse waves the displacement is perpendicular to the direction of propagation of the wave, while in longitudinal waves the displacement is parallel to the direction of propagation.

Question 12

Water waves in the sea are observed to have a wavelength of 300 m and a frequency of 0.07 Hz.The speed of these waves is:

Accepted Answer

A) 0.00023 m/s 
B) 2.1 m/s 
C) 21 m/s 
D) 4300 m/s 
E) none of these 
A) 0.00023 m/s 
B) 2.1 m/s 
C) 21 m/s 
D) 4300 m/s 
E) none of these

Question 13

This plot shows the displacement of a string as a function of time, as a sinusoidal wave travels along it.Which letter corresponds to the period 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 14

Which of the following represents the motion of a string element at an antinode of a standing wave?

Accepted Answer

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

Question 15

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

Question 16

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 17

A wave on a string is reflected from a fixed end.The reflected wave:

Accepted Answer

A) is in phase with the original wave at the end 
B) is 180 $\degree$ out of phase with the original wave at the end 
C) has a larger amplitude than the original wave 
D) has a larger speed than the original wave 
E) cannot be transverse 
A) is in phase with the original wave at the end 
B) is 180 $\degree$ out of phase with the original wave at the end 
C) has a larger amplitude than the original wave 
D) has a larger speed than the original wave 
E) cannot be transverse

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

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 20

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

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:

The time required for a small pulse to travel from A to B on a stretched cord shown is NOT altered by changing:

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:

In the diagram below, the interval PQ represents:

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:

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

Two traveling sinusoidal waves interfere to produce a wave with the mathematical form If the value of ϕ\phiϕ is appropriately chosen, the two waves might be:

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:

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:

Fully constructive interference between two sinusoidal waves of the same frequency occurs only if they:

What is the difference between transverse and longitudinal waves?

Water waves in the sea are observed to have a wavelength of 300 m and a frequency of 0.07 Hz.The speed of these waves is:

This plot shows the displacement of a string as a function of time, as a sinusoidal wave travels along it.Which letter corresponds to the period of the wave?

Which of the following represents the motion of a string element at an antinode of a standing wave?

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 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 wave on a string is reflected from a fixed end.The reflected wave:

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

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:

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:

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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:

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:

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