Question 1

The superposition of two waves  
And  
At the location x = 0 in space results in

Accepted Answer

A) beats at a beat frequency of 3 Hz. 
B) a pure tone at a frequency of 153 Hz. 
C) a pure tone at a frequency of 156 Hz. 
D) beats at a beat frequency of 6 Hz in a 153 Hz tone. 
E) a tone at a frequency of 156 Hz,as well as beats at a beat frequency of 6 Hz in a 153 Hz tone. 
A) beats at a beat frequency of 3 Hz. 
B) a pure tone at a frequency of 153 Hz. 
C) a pure tone at a frequency of 156 Hz. 
D) beats at a beat frequency of 6 Hz in a 153 Hz tone. 
E) a tone at a frequency of 156 Hz,as well as beats at a beat frequency of 6 Hz in a 153 Hz tone.

Question 2

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 3

An organ pipe open at both ends is 1.5 m long.A second organ pipe that is closed at one end and open at the other is 0.75 m long.The speed of sound in the room is 330 m/s.Which of the following sets of frequencies consists of frequencies which can be produced by both pipes?

Accepted Answer

A) 110 Hz,220 Hz,330 Hz 
B) 220 Hz,440 Hz,660 Hz 
C) 110 Hz,330 Hz,550 Hz 
D) 330 Hz,440 Hz,550 Hz 
E) 220 Hz,660 Hz,1 100 Hz 
A) 110 Hz,220 Hz,330 Hz 
B) 220 Hz,440 Hz,660 Hz 
C) 110 Hz,330 Hz,550 Hz 
D) 330 Hz,440 Hz,550 Hz 
E) 220 Hz,660 Hz,1 100 Hz

Question 4

A string is stretched and fixed at both ends,200 cm apart.If the density of the string is 0.015 g/cm,and its tension is 600 N,what is the fundamental frequency?

Accepted Answer

A) 316 Hz 
B) 632 Hz 
C) 158 Hz 
D) 215 Hz 
E) 79 Hz 
A) 316 Hz 
B) 632 Hz 
C) 158 Hz 
D) 215 Hz 
E) 79 Hz

Question 5

Two waves are described by
Y1 = 6 cos 180t and y2 = 6 cos 186t, (both in meters).
What effective frequency does the resultant vibration have at a point?

Accepted Answer

A) 92 Hz 
B) 183 Hz 
C) 6 Hz 
D) 3 Hz 
E) 366 Hz 
A) 92 Hz 
B) 183 Hz 
C) 6 Hz 
D) 3 Hz 
E) 366 Hz

Question 6

Two tuning forks with frequencies 264 and 262 Hz produce "beats".What is the beat frequency (in Hz)?

Accepted Answer

A) 4 
B) 2 
C) 1 
D) 3 
E) 0 (no beats are produced) 
A) 4 
B) 2 
C) 1 
D) 3 
E) 0 (no beats are produced)

Question 7

A clarinet behaves like a tube closed at one end.If its length is 1.0 m,and the velocity of sound is 344 m/s,what is its fundamental frequency (in Hz)?

Accepted Answer

A) 264 
B) 140 
C) 86 
D) 440 
E) 172 
A) 264 
B) 140 
C) 86 
D) 440 
E) 172

Question 8

A student wants to establish a standing wave on a wire 1.8 m long clamped at both ends.The wave speed is 540 m/s.What is the minimum frequency she should apply to set up standing waves?

Accepted Answer

The answer of A student wants to establish a standing...

Question 9

Two organ pipes,a pipe of fundamental frequency 440 Hz,closed at one end,and a pipe of fundamental frequency 660 Hz,open at both ends,produce overtones.Which choice below correctly describes overtones present in both pipes?

Accepted Answer

A) After the first overtone of each pipe,every second overtone of the first pipe matches every second overtone of the second pipe. 
B) After the first overtone of each pipe,every second overtone of the first pipe matches every third overtone of the second pipe. 
C) After the first overtone of each pipe,every third overtone of the first pipe matches every second overtone of the second pipe. 
D) After the first overtone of each pipe,every second overtone of the first pipe matches every fourth overtone of the second pipe. 
E) After the first overtone of each pipe,every third overtone of the first pipe matches every fourth overtone of the second pipe. 
A) After the first overtone of each pipe,every second overtone of the first pipe matches every second overtone of the second pipe. 
B) After the first overtone of each pipe,every second overtone of the first pipe matches every third overtone of the second pipe. 
C) After the first overtone of each pipe,every third overtone of the first pipe matches every second overtone of the second pipe. 
D) After the first overtone of each pipe,every second overtone of the first pipe matches every fourth overtone of the second pipe. 
E) After the first overtone of each pipe,every third overtone of the first pipe matches every fourth overtone of the second pipe.

Question 10

Two harmonic waves traveling in opposite directions interfere to produce a standing wave described by y = 3 sin (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 11

Tuning forks #1,#2,and #3 each have slightly different frequencies.When #1 and #2 are sounded together,a beat frequency of 3 Hz results.When #2 and #3 are sounded together,a beat frequency of 5 Hz results.If the frequency of #1 is 100 Hz,which of the following cannot be the frequency of #3?

Accepted Answer

A) 92 Hz 
B) 95 Hz 
C) 98 Hz 
D) 102 Hz 
E) 108 Hz 
A) 92 Hz 
B) 95 Hz 
C) 98 Hz 
D) 102 Hz 
E) 108 Hz

Question 12

The path difference between two waves is 5m.If the wavelength of the waves emitted by the two sources is 4m,what is the phase difference (in degrees)?

Accepted Answer

A) 90 
B) 400 
C) 1.57 
D) 7.85 
E) 15 
A) 90 
B) 400 
C) 1.57 
D) 7.85 
E) 15

Question 13

A string with a fixed frequency vibrator at one end is undergoing resonance with 4 antinodes when under tension T1.When the tension is slowly increased the resonance condition disappears until tension T2 is reached,there being no resonances occurring between these two tensions.How many antinodes are there in this new resonance?

Accepted Answer

A) 3 
B) 4,since all resonances in this situation have the same number of nodes 
C) 5 
D) 2,since resonances only involve whole wavelengths 
E) 6,since resonances only involve whole wavelength 
A) 3 
B) 4,since all resonances in this situation have the same number of nodes 
C) 5 
D) 2,since resonances only involve whole wavelengths 
E) 6,since resonances only involve whole wavelength

Question 14

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 15

Two waves are described by
Y1 = 6 cos 180t and y2 = 6 cos 186t, (both in meters).
With what angular frequency does the maximum amplitude of the resultant wave vary with time?

Accepted Answer

A) 366 rad/s 
B) 6 rad/s 
C) 3 rad/s 
D) 92 rad/s 
E) 180 rad/s 
A) 366 rad/s 
B) 6 rad/s 
C) 3 rad/s 
D) 92 rad/s 
E) 180 rad/s

Question 16

Which of the following frequencies could NOT be present as a standing wave in a 2m 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

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 18

A harmonic longitudinal wave propagating down a tube filled with a compressible gas has the form s(x,t)= sm cos (kx − ωt).Its velocity can be obtained from

Accepted Answer

A) ω/k 
B) k/ω 
C) k 
D) ω 
E) ωk 
A) ω/k 
B) k/ω 
C) k 
D) ω 
E) ωk

Question 19

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 20

Drummers like to have high-pitched cymbals that vibrate at high frequencies.To obtain the highest frequencies,a cymbal of a fixed size should be made of a material

Accepted Answer

A) with a low Young's modulus and a low density. 
B) with a low Young's modulus and a high density. 
C) with a high Young's modulus and a low density. 
D) with a high Young's modulus and a high density. 
E) composed of a metal-plastic laminate. 
A) with a low Young's modulus and a low density. 
B) with a low Young's modulus and a high density. 
C) with a high Young's modulus and a low density. 
D) with a high Young's modulus and a high density. 
E) composed of a metal-plastic laminate.

Exam 18: Superposition and Standing Waves

The superposition of two waves And At the location x = 0 in space results in

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?

An organ pipe open at both ends is 1.5 m long.A second organ pipe that is closed at one end and open at the other is 0.75 m long.The speed of sound in the room is 330 m/s.Which of the following sets of frequencies consists of frequencies which can be produced by both pipes?

A string is stretched and fixed at both ends,200 cm apart.If the density of the string is 0.015 g/cm,and its tension is 600 N,what is the fundamental frequency?

Two waves are described by Y1 = 6 cos 180t and y2 = 6 cos 186t, (both in meters). What effective frequency does the resultant vibration have at a point?

Two tuning forks with frequencies 264 and 262 Hz produce "beats".What is the beat frequency (in Hz)?

A clarinet behaves like a tube closed at one end.If its length is 1.0 m,and the velocity of sound is 344 m/s,what is its fundamental frequency (in Hz)?

A student wants to establish a standing wave on a wire 1.8 m long clamped at both ends.The wave speed is 540 m/s.What is the minimum frequency she should apply to set up standing waves?

Two organ pipes,a pipe of fundamental frequency 440 Hz,closed at one end,and a pipe of fundamental frequency 660 Hz,open at both ends,produce overtones.Which choice below correctly describes overtones present in both pipes?

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

Tuning forks #1,#2,and #3 each have slightly different frequencies.When #1 and #2 are sounded together,a beat frequency of 3 Hz results.When #2 and #3 are sounded together,a beat frequency of 5 Hz results.If the frequency of #1 is 100 Hz,which of the following cannot be the frequency of #3?

The path difference between two waves is 5m.If the wavelength of the waves emitted by the two sources is 4m,what is the phase difference (in degrees)?

Superposition of waves can occur

Two waves are described by Y1 = 6 cos 180t and y2 = 6 cos 186t, (both in meters). With what angular frequency does the maximum amplitude of the resultant wave vary with time?

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

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)?

A harmonic longitudinal wave propagating down a tube filled with a compressible gas has the form s(x,t)= sm cos (kx − ωt).Its velocity can be obtained from

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?

Drummers like to have high-pitched cymbals that vibrate at high frequencies.To obtain the highest frequencies,a cymbal of a fixed size should be made of a material

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Two waves are described by Y₁ = 6 cos 180t and y₂ = 6 cos 186t, (both in meters). What effective frequency does the resultant vibration have at a point?

Two waves are described by Y₁ = 6 cos 180t and y₂ = 6 cos 186t, (both in meters). With what angular frequency does the maximum amplitude of the resultant wave vary with time?

A harmonic longitudinal wave propagating down a tube filled with a compressible gas has the form s(x,t)= s_m cos (kx − ωt).Its velocity can be obtained from