Question 1

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)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 2

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 3

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 4

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 5

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 6

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

When the incident pulse reaches the splice, it will create a reflected pulse that travels up the rope. The reflected pulse will experience a phase shift of 180 degrees at the splice due to the change in direction of the rope, and will be inverted. This means that the top and bottom sections of the rope will switch places, so the correct answer is C.

Question 7

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 8

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 9

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

To obtain high frequencies, the material should have a high stiffness (high Young's modulus) to allow for high vibration frequencies. At the same time, it should be light (low density) to allow for a high vibration amplitude. Therefore, the best choice is a material with a high Young's modulus and a low density, which is option C.

Question 10

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
A)ω/k
B)k/ω
C)k
D)ω
E)ωk

Accepted Answer

The velocity of a wave is given by v=ω/k, where ω is the angular frequency (2πf) and k is the wave number (2π/λ), where λ is the wavelength. Since s(x, t) = smcos(kx − ωt) represents a longitudinal wave in a compressible gas, we know that the wave speed is given by v=√(γP/ρ), where γ is the ratio of specific heats, P is the pressure of the gas, and ρ is its density. Therefore, we can equate v=ω/k to get:
v=ω/k = √(γP/ρ)
Simplifying, we get:
ω/k = √(γP/ρ)
ω = k√(γP/ρ)
The only answer choice that matches this expression is A: ω/k.

Question 11

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 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

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)?

Accepted Answer

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

Question 14

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 both transverse and longitudinal waves, as well as sinusoidal waves. Therefore, option D is the correct choice. Option E, which suggests that superposition only occurs in transverse and sinusoidal waves, is incorrect.

Question 15

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)0.
B)  .
C)π.
D)  .
E)2π

Accepted Answer

The answer of 
The figure below shows wave crests after...

Question 16

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...

Quiz 18: Superposition and Standing Waves

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 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?

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 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 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 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?

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.

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 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

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

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)?

Superposition of waves can occur

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

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?