Question 1

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 C

Question 2

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

Accepted Answer

A)    m.
B)  2 m.
C)  π m.
D)  4 m.
E)  4π m. D

Question 3

Two waves are described by ​
Y1 = 6cos(180t) and y2 = 6cos(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 C

Question 4

An observer stands 3 m from speaker A and 4 m from speaker B. Both speakers, oscillating in phase, produce 170-Hz waves. The speed of sound in air is 340 m/s. What is the phase difference (in radians) between the waves from A and B at the observer's location, point P? ​  ​

Accepted Answer

A)  0
B)   
C)  π
D)  2π
E)  4π

Question 5

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

Question 6

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.
E)  beats at a frequency of 156 Hz.

Question 7

A string with a fixed frequency vibrator at one end is subjected to varying tensions. When the tension is 20 N, a resonance with 3 antinodes results. What tension would cause a resonance with 2 antinodes in this string?

Accepted Answer

A)  30 N
B)  45 N
C)  80 N
D)  8.9 N
E)  13 N

Question 8

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

Question 9

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

Question 10

Two harmonic waves are described by   From the choices given, determine the smallest positive value of x (in cm) corresponding to a node of the resultant standing wave.

Accepted Answer

A)  3
B)  0.25
C)  0
D)  6
E)  1.5

Question 11

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

Accepted Answer

A)  ω/k
B)  k/ω
C)  k
D)  ω
E)  ωk

Question 12

In a standing wave, not necessarily at the fundamental frequency, on a string of length L, the distance between nodes is

Accepted Answer

A)  λ/4.
B)  λ/2.
C)  λ.
D)  L/4.
E)  L/2.

Question 13

Two harmonic waves traveling in opposite directions interfere to produce a standing wave described by y = 2sin(πx)cos(3πt), where x is in m and t is in s. What is the distance (in m) between the first two antinodes?

Accepted Answer

A)  8
B)  2
C)  4
D)  1
E)  0.5

Question 14

The figure below shows the positions of particles in a longitudinal standing wave. One quarter period later the particle distribution is shown in

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 15

Two harmonic waves traveling in opposite directions interfere to produce a standing wave described by y = 4sin(5x)cos(6t) where x is in m and t is in s. What is the approximate frequency of the interfering waves?

Accepted Answer

A)  3 Hz
B)  1 Hz
C)  6 Hz
D)  12 Hz
E)  5 Hz

Question 16

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

Accepted Answer

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

Question 17

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

Question 18

Two strings are, respectively, 1.00 m and 2.00 m long. Which of the following wavelengths, in meters, could represent harmonics present on both strings?

Accepted Answer

A)  0.800, 0.670, 0.500
B)  1.33, 1.00, 0.500
C)  2.00, 1.00, 0.500
D)  2.00, 1.33, 1.00
E)  4.00, 2.00, 1.00

Question 19

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.

Question 20

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...

Exam 18: Superposition and Standing Waves

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?

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

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

An observer stands 3 m from speaker A and 4 m from speaker B. Both speakers, oscillating in phase, produce 170-Hz waves. The speed of sound in air is 340 m/s. What is the phase difference (in radians) between the waves from A and B at the observer's location, point P?

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

A string with a fixed frequency vibrator at one end is subjected to varying tensions. When the tension is 20 N, a resonance with 3 antinodes results. What tension would cause a resonance with 2 antinodes in this string?

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) ?

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?

Two harmonic waves are described by From the choices given, determine the smallest positive value of x (in cm) corresponding to a node of the resultant standing wave.

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

In a standing wave, not necessarily at the fundamental frequency, on a string of length L, the distance between nodes is

Two harmonic waves traveling in opposite directions interfere to produce a standing wave described by y = 2sin(πx) cos(3πt) , where x is in m and t is in s. What is the distance (in m) between the first two antinodes?

The figure below shows the positions of particles in a longitudinal standing wave. One quarter period later the particle distribution is shown in

Two harmonic waves traveling in opposite directions interfere to produce a standing wave described by y = 4sin(5x) cos(6t) where x is in m and t is in s. What is the approximate frequency of the interfering waves?

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

Two strings are, respectively, 1.00 m and 2.00 m long. Which of the following wavelengths, in meters, could represent harmonics present on both strings?

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

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?

Exam 18: Superposition and Standing Waves

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?

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

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

An observer stands 3 m from speaker A and 4 m from speaker B. Both speakers, oscillating in phase, produce 170-Hz waves. The speed of sound in air is 340 m/s. What is the phase difference (in radians) between the waves from A and B at the observer's location, point P? ​ ​

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 superposition of two waves ​ and ​ At the location x = 0 in space results in

A string with a fixed frequency vibrator at one end is subjected to varying tensions. When the tension is 20 N, a resonance with 3 antinodes results. What tension would cause a resonance with 2 antinodes in this string?

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) ?

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?

Two harmonic waves are described by From the choices given, determine the smallest positive value of x (in cm) corresponding to a node of the resultant standing wave.

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

In a standing wave, not necessarily at the fundamental frequency, on a string of length L, the distance between nodes is

Two harmonic waves traveling in opposite directions interfere to produce a standing wave described by y = 2sin(πx) cos(3πt) , where x is in m and t is in s. What is the distance (in m) between the first two antinodes?

The figure below shows the positions of particles in a longitudinal standing wave. One quarter period later the particle distribution is shown in

Two harmonic waves traveling in opposite directions interfere to produce a standing wave described by y = 4sin(5x) cos(6t) where x is in m and t is in s. What is the approximate frequency of the interfering waves?

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

Two strings are, respectively, 1.00 m and 2.00 m long. Which of the following wavelengths, in meters, could represent harmonics present on both strings?

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

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

An observer stands 3 m from speaker A and 4 m from speaker B. Both speakers, oscillating in phase, produce 170-Hz waves. The speed of sound in air is 340 m/s. What is the phase difference (in radians) between the waves from A and B at the observer's location, point P?

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