Question 1

Which of the following wavelengths could NOT be present as a standing wave in a 2-m-long organ pipe open at both ends?

Accepted Answer

A) 4 m 
B) 2 m 
C) 1 m 
D) 0.89 m 
E) 0.5 m 
A) 4 m 
B) 2 m 
C) 1 m 
D) 0.89 m 
E) 0.5 m

Question 2

Two point sources emit sound waves of 1.0-m wavelength. The sources, 2.0 m apart, as shown below, emit waves which are in phase with each other at the instant of emission. Where, along the line between the sources, are the waves out of phase with each other by π radians?

Accepted Answer

A) x = 0, 1.0 m, 2.0 m 
B) x = 0.50 m, 1.5 m 
C) x = 0.50 m, 1.0 m, 1.5 m 
D) x = 0.75 m, 1.25 m 
E) x = 0.25 m, 0.75 m, 1.25 m, 1.75 m 
A) x = 0, 1.0 m, 2.0 m 
B) x = 0.50 m, 1.5 m 
C) x = 0.50 m, 1.0 m, 1.5 m 
D) x = 0.75 m, 1.25 m 
E) x = 0.25 m, 0.75 m, 1.25 m, 1.75 m

Question 3

The figure below shows wave crests after a stone is thrown into a pond.   Use this exhibit to answer the following question(s).
-The phase difference in radians between points A and D is

Accepted Answer

A) π. 
B) 2π. 
C) 3π. 
D) 4π. 
E) 5π. 
A) π. 
B) 2π. 
C) 3π. 
D) 4π. 
E) 5π.

Question 4

A stretched string is observed to vibrate in three equal segments when driven by a 480-Hz oscillator. What is the fundamental frequency of vibration for this string?

Accepted Answer

A) 480 Hz 
B) 320 Hz 
C) 160 Hz 
D) 640 Hz 
E) 240 Hz 
A) 480 Hz 
B) 320 Hz 
C) 160 Hz 
D) 640 Hz 
E) 240 Hz

Question 5

The superposition of two waves,   and   , results in a wave with a frequency of

Accepted Answer

A) 85 Hz. 
B) 170 Hz. 
C) 85π Hz. 
D) 340 Hz. 
E) 170π Hz. 
A) 85 Hz. 
B) 170 Hz. 
C) 85π Hz. 
D) 340 Hz. 
E) 170π Hz.

Question 6

A very long string is tied to a rigid wall at one end while the other end is attached to a simple harmonic oscillator. Which of the following can be changed by changing the frequency of the oscillator?

Accepted Answer

A) The speed of the waves traveling along the string. 
B) The tension in the string. 
C) The wavelength of the waves on the string. 
D) All of the above. 
E) None of the above. 
A) The speed of the waves traveling along the string. 
B) The tension in the string. 
C) The wavelength of the waves on the string. 
D) All of the above. 
E) None of the above.

Question 7

Superposition of waves can occur

Accepted Answer

A) in transverse waves. 
B) in longitudinal waves. 
C) in sinusoidal waves. 
D) in all of the above. 
E) only in (a) and (c) above. 
A) in transverse waves. 
B) in longitudinal waves. 
C) in sinusoidal waves. 
D) in all of the above. 
E) only in (a) and (c) above.

Question 8

Two pulses are traveling towards each other at 10 cm/s on a long string at t = 0 s, as shown below.   Which diagram below correctly shows the shape of the string at 0.5 s?

Accepted Answer

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

Question 9

The superposition of two waves,   and   , results in a wave with a phase angle of

Accepted Answer

A) 0 rad. 
B) 0.5 rad. 
C)    rad. 
D)    rad. 
E) π rad. 
A) 0 rad. 
B) 0.5 rad. 
C)    rad. 
D)    rad. 
E) π rad.

Question 10

The figure below shows wave crests after a stone is thrown into a pond.   Use this exhibit to answer the following question(s).
-The phase difference in radians between points A and C is

Accepted Answer

A) 0. 
B)    . 
C) π. 
D)    . 
E) 2π 
A) 0. 
B)    . 
C) π. 
D)    . 
E) 2π

Question 11

A vertical tube one meter long is open at the top. It is filled with 75 cm of water. If the velocity of sound is 344 m/s, what will the fundamental resonant frequency be (in Hz)?

Accepted Answer

A) 3.4 
B) 172 
C) 344 
D) 1.7 
E) 688 
A) 3.4 
B) 172 
C) 344 
D) 1.7 
E) 688

Question 12

Two harmonic waves traveling in opposite directions interfere to produce a standing wave described by y = 2sin(4x)cos(3t), where x is in m and t is in s. What is the speed (in m/s) of the interfering waves?

Accepted Answer

A) 0.75 
B) 0.25 
C) 1.3 
D) 12 
E) 3.0 
A) 0.75 
B) 0.25 
C) 1.3 
D) 12 
E) 3.0

Question 13

Which of the following wavelengths could NOT be present as a harmonic on a 2-m-long string?

Accepted Answer

A) 4 m 
B) 2 m 
C) 1 m 
D) 0.89 m 
E) 0.5 m 
A) 4 m 
B) 2 m 
C) 1 m 
D) 0.89 m 
E) 0.5 m

Question 14

An organ pipe open at both ends has a radius of 4.0 cm and a length of 6.0 m. What is the frequency (in Hz) of the third harmonic? (Assume the velocity of sound is 344 m/s.)

Accepted Answer

A) 76 
B) 86 
C) 54 
D) 28 
E) 129 
A) 76 
B) 86 
C) 54 
D) 28 
E) 129

Question 15

Find the frequencies of the first three harmonics of a 1.0-m long string which has a mass per unit length of 2.0 × 10−3 kg/m and a tension of 80 N when both ends are fixed in place.

Accepted Answer

100 Hz, 20

Question 16

Which of the following frequencies could NOT be present as a standing wave in a 2-m-long organ pipe open at both ends? The fundamental frequency is 85 Hz.

Accepted Answer

A) 85 Hz. 
B) 170 Hz. 
C) 255 Hz. 
D) 340 Hz. 
E) 382 Hz. 
A) 85 Hz. 
B) 170 Hz. 
C) 255 Hz. 
D) 340 Hz. 
E) 382 Hz.

Question 17

Two harmonic waves traveling in opposite directions interfere to produce a standing wave described by y = 3sin(2x)cos(5t​), where x is in m and t is in s. What is the wavelength of the interfering waves?

Accepted Answer

A) 3.14 m 
B) 1.00 m 
C) 6.28 m 
D) 12.0 m 
E) 2.00 m 
A) 3.14 m 
B) 1.00 m 
C) 6.28 m 
D) 12.0 m 
E) 2.00 m

Question 18

A fire engine approaches a wall at 5 m/s while the siren emits a tone of 500-Hz frequency. At the time, the speed of sound in air is 340 m/s. How many beats per second do the people on the fire engine hear?

Accepted Answer

A) 0 
B) 15 
C) 29 
D) 63 
E) 250 
A) 0 
B) 15 
C) 29 
D) 63 
E) 250

Question 19

As shown below, a garden room has three walls, a floor, and a roof, but is open to the garden on one side. The wall widths are L and w. The roof height is h. When traveling sound waves enter the room, standing sound waves can be present in the room if the wavelength of the standing waves is ​   ​

Accepted Answer

A)    , where n is a positive integer. 
B)    , where n is an odd integer. 
C)    , where n is an even integer. 
D) in all cases listed above. 
E) given by (a) or (b) above, but not by (c). 
A)    , where n is a positive integer. 
B)    , where n is an odd integer. 
C)    , where n is an even integer. 
D) in all cases listed above. 
E) given by (a) or (b) above, but not by (c).

Question 20

Two speakers in an automobile emit sound waves that are in phase at the speakers. One speaker is 40 cm ahead of and 30 cm to the left of the driver's left ear. The other speaker is 50 cm ahead of and 120 cm to the right of the driver's right ear. Which of the following wavelengths is(are) in phase at the left ear for the speaker on the left and the right ear for the speaker on the right?

Accepted Answer

A) 10 cm 
B) 20 cm 
C) 650 cm 
D) All of the wavelengths listed above. 
E) Only the wavelengths listed in (a) and (b). 
A) 10 cm 
B) 20 cm 
C) 650 cm 
D) All of the wavelengths listed above. 
E) Only the wavelengths listed in (a) and (b).

Exam 18: Superposition and Standing Waves

Which of the following wavelengths could NOT be present as a standing wave in a 2-m-long organ pipe open at both ends?

Two point sources emit sound waves of 1.0-m wavelength. The sources, 2.0 m apart, as shown below, emit waves which are in phase with each other at the instant of emission. Where, along the line between the sources, are the waves out of phase with each other by π radians?

The figure below shows wave crests after a stone is thrown into a pond. Use this exhibit to answer the following question(s). -The phase difference in radians between points A and D is

A stretched string is observed to vibrate in three equal segments when driven by a 480-Hz oscillator. What is the fundamental frequency of vibration for this string?

The superposition of two waves, and , results in a wave with a frequency of

A very long string is tied to a rigid wall at one end while the other end is attached to a simple harmonic oscillator. Which of the following can be changed by changing the frequency of the oscillator?

Superposition of waves can occur

Two pulses are traveling towards each other at 10 cm/s on a long string at t = 0 s, as shown below. Which diagram below correctly shows the shape of the string at 0.5 s?

The superposition of two waves, and , results in a wave with a phase angle of

The figure below shows wave crests after a stone is thrown into a pond. Use this exhibit to answer the following question(s). -The phase difference in radians between points A and C is

A vertical tube one meter long is open at the top. It is filled with 75 cm of water. If the velocity of sound is 344 m/s, what will the fundamental resonant frequency be (in Hz)?

Two harmonic waves traveling in opposite directions interfere to produce a standing wave described by y = 2sin(4x)cos(3t), where x is in m and t is in s. What is the speed (in m/s) of the interfering waves?

Which of the following wavelengths could NOT be present as a harmonic on a 2-m-long string?

An organ pipe open at both ends has a radius of 4.0 cm and a length of 6.0 m. What is the frequency (in Hz) of the third harmonic? (Assume the velocity of sound is 344 m/s.)

Find the frequencies of the first three harmonics of a 1.0-m long string which has a mass per unit length of 2.0 × 10−3 kg/m and a tension of 80 N when both ends are fixed in place.

Which of the following frequencies could NOT be present as a standing wave in a 2-m-long organ pipe open at both ends? The fundamental frequency is 85 Hz.

Two harmonic waves traveling in opposite directions interfere to produce a standing wave described by y = 3sin(2x)cos(5t​), where x is in m and t is in s. What is the wavelength of the interfering waves?

A fire engine approaches a wall at 5 m/s while the siren emits a tone of 500-Hz frequency. At the time, the speed of sound in air is 340 m/s. How many beats per second do the people on the fire engine hear?

As shown below, a garden room has three walls, a floor, and a roof, but is open to the garden on one side. The wall widths are L and w. The roof height is h. When traveling sound waves enter the room, standing sound waves can be present in the room if the wavelength of the standing waves is ​ ​

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Two harmonic waves traveling in opposite directions interfere to produce a standing wave described by y = 3sin(2x)cos(5t), where x is in m and t is in s. What is the wavelength of the interfering waves?

As shown below, a garden room has three walls, a floor, and a roof, but is open to the garden on one side. The wall widths are L and w. The roof height is h. When traveling sound waves enter the room, standing sound waves can be present in the room if the wavelength of the standing waves is