Question 1

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

The answer of Find the frequencies of the first three...

Question 2

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 A) ω/k B) k/ω C) k D) ω E) ωk

Accepted Answer

The velocity of a longitudinal wave in a compressible gas is given by v = √(γP/ρ), where γ is the adiabatic index, P is the pressure, and ρ is the density of the gas.

For a harmonic longitudinal wave, we have k = 2π/λ = ω/v, where λ is the wavelength and ω is the angular frequency.

Thus, v = ω/k = ω/(2π/λ) = λω/(2π) = ω/k.

Therefore, the best choice is A.

Question 3

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

Accepted Answer

The answer of Tuning forks #1, #2, and #3 each...

Question 4

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

B)

C)

D)

E)

Accepted Answer

The answer of The figure below shows the positions of...

Question 5

Exhibit 18-1
The figure below shows wave crests after a stone is thrown into a pond.  Use this exhibit to answer the following question(s).
-Refer to Exhibit 18-1. The phase difference in radians between points A and B is
A) 0.
B)
 .
C)
 .
D) π.
E)
 .

Accepted Answer

The answer of Exhibit 18-1
The figure below shows wave crests...

Question 6

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?
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.

Accepted Answer

The answer of Two organ pipes, a pipe of fundamental...

Question 7

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?
A)

B)

C)

D)

E)

Accepted Answer

The answer of Two pulses are traveling towards each other...

Question 8

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

Accepted Answer

The frequency of a vibrating string is given by:
f = (1/2L) * sqrt(T/u)
where L is the length of the string, T is the tension, and u is the linear density of the string. Since the linear density is not changing, we can assume that it is constant.
If we have a resonance with 3 antinodes, then the wavelength is equal to twice the length of the string. This means that:
wavelength = 2L = 3/2 * length of string
We can rearrange the frequency equation to solve for tension:
T = (4f^2 * L^2 * u) / 1
If we plug in the values for a resonance with 3 antinodes, we get:
20 = (4f^2 * L^2 * u) / 1
If we plug in the values for a resonance with 2 antinodes, we get:
T = (4f^2 * L^2 * u) / (3/4)
We want to find the tension that causes a resonance with 2 antinodes. Since L and u are constant for this string, we can simplify this equation to:
T = (16/3) * f^2 * L^2 * u
We can solve for T by dividing this equation by the first equation:
T (2 antinodes) / T (3 antinodes) = 16/3
T (2 antinodes) = (16/3) * T (3 antinodes)
T (2 antinodes) = (16/3) * 20 = 106.7
Rounding to the nearest option gives us:
Answer: B

Question 9

Superposition of waves can occur
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.

Accepted Answer

Superposition of waves can occur in all types of waves, including transverse, longitudinal, and sinusoidal waves. It is a fundamental property of waves and occurs when two or more waves overlap, resulting in the combination of their displacements.

Question 10

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? 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

Accepted Answer

The answer of A string with a fixed frequency vibrator...

Question 11

Exhibit 18-1
The figure below shows wave crests after a stone is thrown into a pond.  Use this exhibit to answer the following question(s).
-Refer to Exhibit 18-1. The phase difference in radians between points A and C is
A) 0.
B)
 .
C) π.
D)
 .
E) 2π

Accepted Answer

The answer of Exhibit 18-1
The figure below shows wave crests...

Question 12

Two ropes are spliced together as shown.  A short time after the incident pulse shown in the diagram reaches the splice, the rope's appearance will be that in
A)

B)

C)

D)

E)

Accepted Answer

The answer of Two ropes are spliced together as shown....

Question 13

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) 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.

Accepted Answer

The frequency of vibration of a cymbal depends on its mass and stiffness, which means that it depends on the material properties of the cymbal. A material with a high Young's modulus (which measures the stiffness of a material) will allow the cymbal to vibrate at higher frequencies. Additionally, a material with a low density will result in a lighter cymbal, which will also vibrate at higher frequencies. Therefore, the best choice is a material with a high Young's modulus and a low density, which is answer choice C.

Question 14

Two ropes are spliced together as shown.  A short time after the incident pulse shown in the diagram reaches the splice, the rope's appearance will be that in
A)

B)

C)

D)

E)

Accepted Answer

The answer of Two ropes are spliced together as shown....

Question 15

A steel wire in a piano has a length of 0.700 m and a mass of 4.30 grams. To what tension must this wire be stretched to make the fundamental frequency correspond to middle C, (f_c = 261.6 Hz)?

Accepted Answer

The answer of A steel wire in a piano has...

Question 16

When two organ pipes each closed at one end sound a perfect fifth, such as two notes with fundamental frequencies at 440 Hz and 660 Hz, both pipes produce overtones. Which choice below correctly describes overtones present in both pipes?
A) 440, 880 and 1 320 Hz.
B) 660, 1 320 and 1 980 Hz.
C) 880, 1 320 and 1 760 Hz.
D) 1 320, 2 640 and 3 960 Hz.
E) They have no overtones in common.

Accepted Answer

Organ pipes closed at one end produce odd harmonics only. The first pipe with a fundamental frequency of 440 Hz will produce overtones at 3*440 = 1320 Hz, 5*440 = 2200 Hz, etc. The second pipe with a fundamental frequency of 660 Hz will produce overtones at 3*660 = 1980 Hz, 5*660 = 3300 Hz, etc. Since the overtones are based on odd multiples of the fundamental frequency, and the fundamental frequencies of the two pipes are not multiples of each other, they do not share any common overtones.

Question 17

When two organ pipes open at both ends sound a perfect fifth, such as two notes with fundamental frequencies at 440 Hz and 660 Hz, both pipes produce overtones. Which choice below correctly describes overtones present in both pipes?
A) 440, 880 and 1 320 Hz.
B) 660, 1 320 and 1 980 Hz.
C) 880, 1 320 and 1 760 Hz.
D) 1 320, 2 640 and 3 960 Hz.
E) They have no overtones in common.

Accepted Answer

The answer of When two organ pipes open at both...

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

Accepted Answer

The answer of A fire engine approaches a wall at...

Question 19

Exhibit 18-1
The figure below shows wave crests after a stone is thrown into a pond.  Use this exhibit to answer the following question(s).
-Refer to Exhibit 18-1. The phase difference in radians between points A and D is
A) π.
B) 2π.
C) 3π.
D) 4π.
E) 5π.

Accepted Answer

Points A and D are on opposite sides of a wave crest, which corresponds to a phase difference of π radians. The crest-to-crest distance between A and D is two wavelengths, which corresponds to a phase difference of 2π radians. Therefore, the total phase difference between points A and D is 3π radians.

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...

Quiz 18: Superposition and Standing Waves

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.

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

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

Exhibit 18-1 The figure below shows wave crests after a stone is thrown into a pond. Use this exhibit to answer the following question(s) . -Refer to Exhibit 18-1. The phase difference in radians between points A and B is

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 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?

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?

Superposition of waves can occur

Exhibit 18-1 The figure below shows wave crests after a stone is thrown into a pond. Use this exhibit to answer the following question(s) . -Refer to Exhibit 18-1. The phase difference in radians between points A and C is

Two ropes are spliced together as shown. A short time after the incident pulse shown in the diagram reaches the splice, the rope's appearance will be that in

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

Two ropes are spliced together as shown. A short time after the incident pulse shown in the diagram reaches the splice, the rope's appearance will be that in

A steel wire in a piano has a length of 0.700 m and a mass of 4.30 grams. To what tension must this wire be stretched to make the fundamental frequency correspond to middle C, (f_c = 261.6 Hz)?

When two organ pipes each closed at one end sound a perfect fifth, such as two notes with fundamental frequencies at 440 Hz and 660 Hz, both pipes produce overtones. Which choice below correctly describes overtones present in both pipes?

When two organ pipes open at both ends sound a perfect fifth, such as two notes with fundamental frequencies at 440 Hz and 660 Hz, both pipes produce overtones. Which choice below correctly describes overtones present in both pipes?

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?

Exhibit 18-1 The figure below shows wave crests after a stone is thrown into a pond. Use this exhibit to answer the following question(s) . -Refer to Exhibit 18-1. The phase difference in radians between points A and D is

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?

Quiz 18: Superposition and Standing Waves

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.

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

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

Exhibit 18-1 The figure below shows wave crests after a stone is thrown into a pond. Use this exhibit to answer the following question(s) . -Refer to Exhibit 18-1. The phase difference in radians between points A and B is

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 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?

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?

Superposition of waves can occur

Exhibit 18-1 The figure below shows wave crests after a stone is thrown into a pond. Use this exhibit to answer the following question(s) . -Refer to Exhibit 18-1. The phase difference in radians between points A and C is

Two ropes are spliced together as shown. A short time after the incident pulse shown in the diagram reaches the splice, the rope's appearance will be that in

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

Two ropes are spliced together as shown. A short time after the incident pulse shown in the diagram reaches the splice, the rope's appearance will be that in

A steel wire in a piano has a length of 0.700 m and a mass of 4.30 grams. To what tension must this wire be stretched to make the fundamental frequency correspond to middle C, (fc = 261.6 Hz)?

When two organ pipes each closed at one end sound a perfect fifth, such as two notes with fundamental frequencies at 440 Hz and 660 Hz, both pipes produce overtones. Which choice below correctly describes overtones present in both pipes?

When two organ pipes open at both ends sound a perfect fifth, such as two notes with fundamental frequencies at 440 Hz and 660 Hz, both pipes produce overtones. Which choice below correctly describes overtones present in both pipes?

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?

Exhibit 18-1 The figure below shows wave crests after a stone is thrown into a pond. Use this exhibit to answer the following question(s) . -Refer to Exhibit 18-1. The phase difference in radians between points A and D is

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?

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.

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

A steel wire in a piano has a length of 0.700 m and a mass of 4.30 grams. To what tension must this wire be stretched to make the fundamental frequency correspond to middle C, (f_c = 261.6 Hz)?