Chapter 11
A string of length L and linear mass density μ fixed at both ends resonates in its second harmonic (n = 2). By what factor must the tension magnitude in the string be changed so that the string resonates in its third harmonic (n = 3)?
9/4
Suppose two coherent waves interfere constructively. The amplitude of the first is 2A and the amplitude of the second is also A. If the intensity of the smaller wave is I, what is the intensity of the combined wave?
9I
Which of the following statements is correct?
A wave is sometimes inverted when it reflects.
When does the direction of propagation of a wave change when it crosses a boundary between two media with different wave speeds?
Always, except when the propagation direction is normal to the boundary
Transverse waves are observed on six strings, each of length L. The magnitude of the tension and the linear mass density of each is given. Rank the cases from greatest at the top to least at the bottom based upon the wave speed, and rank all ties alphabetically.
B E A C D F
Select all of the following types of waves that are possible.
Both transverse and longitudinal
What type of waves are ocean waves?
Both transverse and longitudinal
Select all of the following statements that are true
If two waves are 180 degrees out of phase, then they will interfere destructively. If two waves are in phase, then they will interfere constructively.
Select all of the following that are directly proportional to the square of the amplitude of a wave.
Intensity of the wave Total energy carried by the wave Power of the wave
Two identical transverse traveling waves moving to the right are initially in phase. Select all of the following actions that would cause them to become 180 degrees out of phase.
Invert one of the waves. Move one of the waves half a wavelength to the left. Move one of the waves half a wavelength to the right.
Select all of the following statements that are true regarding the intensity of a wave.
It is directly proportional to the average power carried by the wave. It is inversely proportional to the area of the surface perpendicular to the direction of propagation of the wave.
What is a wave?
It's a disturbance that travels away from its source.
Consider two strings fixed at both ends with the same tension magnitude and length but different mass per unit length. Is the fundamental frequency of the string with the larger mass per unit length greater than, equal to, or less than the fundamental frequency of the string with the smaller mass per unit length?
Less than
Select all of the following that are directly proportional to the amplitude of a wave.
Maximum oscillator speed Maximum oscillator acceleration magnitude
Two identical transverse traveling waves moving to the right are initially in phase. Select all of the following actions that would cause them to remain in phase.
Move one of the waves one wavelength to the left. Move one of the waves one wavelength to the right.
What can be determined simply by looking at a graph of displacement versus time of a periodic transverse wave without doing any calculations?
Period
What do we mean if we say waves are incoherent?
The phase difference between them varies randomly.
Select all of the following waves that are periodic.
The sound wave produced when a performer sings the vowel "I" (as in "I write the songs") at a constant frequency The transverse wave produced on a rope when it is swung around repeatedly when "jumping rope"
In the wave function describing a traveling sound wave in air, what does the abbreviation "v" mean?
The speed of the sound wave
Select all of the following that occur during constructive interference.
The troughs of one wave line up with the troughs of the other wave. The crests of one wave line up with the crests of the other wave.
Two waves pulses are identical, except they travel in opposite directions toward each other. They both have positive displacements. Once they occupy the same place at the same time, what will happen?
They'll temporarily combine and make a wave pulse with a larger displacement, then continue moving in their original directions.
True or false: A wave can transmit energy from one point to another without transporting any matter between the two points.
True
Sound waves are emitted from a single speaker and travel through air. Obstacles of various sizes and shapes are located near the speaker. Select all of the following on which the amount of diffraction depends. Assume that the sound travels at a constant speed through the air at all times and in all locations.
Wavelengths of the sound waves Sizes of the obstacles Frequencies of the sound waves
Which of the following statements is true regarding coherent waves?
Waves from the same source are coherent.
Select all of the following statements that are correct.
When a wave reflects from a boundary with a slower wave speed, the reflected wave is inverted. When a wave reflects from a boundary with a faster wave speed, the reflected wave is not inverted. When a wave reflects from a boundary with a faster wave speed, the reflected w
wo or more waves that exist in the same place at the same time can display the phenomenon of interference. Interference is a consequence of the principle and implies that individual wave displacements t every point at every moment in time.
superposition add
The distance a periodic wave travels during one complete cycle is called the
wavelength
A transverse harmonic wave has an amplitude 2.0 cm, a frequency of 500 Hz, and travels through a medium of wave speed 100 m/s. What is the wave function for this wave?
y(x, t) = (0.02 m) sin[ (1000π rad/s)t - (10π rad/m)x]
A transverse harmonic wave has an amplitude 2.0 cm, a frequency of 50 Hz, and travels through a medium of wave speed 100 m/s. What is the wave function for this wave?
y(x, t) = (0.02 m) sin[ (100π rad/s)t - (π rad/m)x]
A transverse harmonic wave has an amplitude 2.0 cm, a frequency of 100 Hz, and travels through a medium of wave speed 100 m/s. What is the wave function for this wave?
y(x, t) = (0.02 m) sin[ (200π rad/s)t - (2π rad/m)x]
Which of the following represents the superposition principle applied to two waves?
y(x, t) = y1(x, t) + y2(x, t)
Select all of the following wave functions that represent waves traveling along the negative x-axis.
y(x,t) = A sin(t + x/v) y(x,t) = A cos(t + x/v)
For harmonic traveling waves, match the quantity on the left with the formula on the right that gives its value.
ω/k ωA w2A
Three strings of different linear mass densities and of equal length are all under the same tension, and their wave speeds have the ratio 1:2:3. What is the ratio of the linear mass densities of the three strings given in the same order?
32:22:12
A string of length L and linear mass density μ fixed at both ends resonates in its second harmonic (n = 2). By what factor must the mass density of the string be changed so that the string resonates in its fundamental mode (n = 1)?
4
By what factor would the intensity of a wave increase if its amplitude doubled?
4
A point on a guitar string vibrates with the displacement versus time graph shown. What is the period of the vibration?
4.0 μs
A water wave is 10 meters tall, that is, the vertical distance from the bottom of the trough to the crest of the wave is 10 meters. What is the amplitude of this wave?
5 meters
What is the wave speed of a 500 Hz wave traveling through a medium with a wavelength of 10 cm?
50 m/s
Two point sources emit 3-D waves that propagate through the same material. Source A produces an intensity at position 2r that is equal to twice the intensity produced by source B at position 4r. What is the ratio of the average power produced by source A to source B?
1/2
Two point sources emit 3-D waves that propagate through the same material. Source A produces an intensity at a distance of 2r that is equal to the intensity produced by source B at a distance of 4r. What is the ratio of the average power output of source A to source B?
1/4
Rank the following harmonic transverse traveling waves on a string in terms of the maximum speed at which a point on the string moves in the transverse direction, with the largest maximum speed at the top and the smallest at the bottom.
10 10m 2 10m 10 10cm 2 10cm
Rank the following water waves according to their amplitudes, with the largest amplitude at the top and the smallest at the bottom. The height is the vertical distance from the bottom of the trough to the crest of the wave.
10 30 20 20 30 10
Rank the following cases according to the intensity of the wave, with the largest intensity at the top and the smallest at the bottom.
10 west 10mm 10 west 10cm 10mw 10mm 10mw 10cm 10w 10m 10mw 10m
Two spherical waves propagate through a medium. The average power carried by the first wave at a distance of 10 m is equal to the average power carried by the second wave at a distance of 100 m. What is the ratio of the intensity of the first wave to the intensity of the second?
100
A transverse harmonic traveling wave is represented by the function y(x, t) = (0.02 m) ⋅ sin [ (1000π rad/s)t - (10π rad/m)x ]. What is the frequency of the wave?
500 Hz
Two spherical waves propagate through a medium. The average power carried by the first wave at a distance of 4 m is equal to the average power carried by the second wave at a distance of 40 m. What is the ratio of the intensity of the first wave to the intensity of the second? Recall that the area of a sphere is 4πr2.
100
A transverse harmonic traveling wave is represented by the function y(x, t) = (0.02 m) ⋅ sin [ (1000π rad/s)t - (10π rad/m)x ]. What is the wave speed?
100 m/s
A string of length L fixed at both ends resonates in one of its modes. Rank the following according to the wavelength of the standing wave on the string, with the largest wavelength at the top and the smallest at the bottom.
10d 1 10d 2 d 1 d 2
A campus radio station operates on a frequency of 100 MHz. What is the period of this radio wave?
10ns
Two waves interfere constructively, that is, they are in phase. The intensity of wave A is nine times the intensity of wave B. What is the intensity of the resulting wave? IA stands for the intensity of wave A and IB stands for the intensity of wave B.
16IB
The displacement versus time and the displacement versus position graphs for a transverse wave are shown. Assume the wave has the form y(x, t) = A sin(ωt - kx). What is the amplitude of the wave?
1m
The displacement versus time and the displacement versus position graphs for a transverse wave are shown. Assume the wave has the form y(x, t) = A sin(ωt - kx). What is the wave speed of the wave?
2.5 m/s
A point on a guitar string vibrates with the displacement versus time graph shown. What is the frequency of the vibration?
250 kHz
A string of length L fixed at both ends resonates in its fundamental mode (n = 1). What is the wavelength of the standing wave on the string?
2L
The displacement versus time and the displacement versus position graphs for a transverse wave are shown. Assume the wave has the form y(x, t) = A sin(ωt - kx). What is the wave number of the wave?
31.4 rad/m
A transverse harmonic traveling wave is represented by the function y(x, t) = (0.02 m) ⋅ sin [ (1000π rad/s)t - (10π rad/m)x ]. What is the wavelength of the wave?
0.2 m
Which term refers to the change in propagation direction (or bending) of a wave (front) when it enters a new medium?
Refraction
Select all of the following waves that are longitudinal.
Seismic P waves Sound waves in air
Sound waves are emitted from a single speaker and travel through air. Obstacles of various sizes and shapes are located near the speaker. Select all of the following on which the amount of diffraction depends. Assume that the sound travels at a constant speed through the air at all times and in all locations.
Sizes of the obstacles Frequencies of the sound waves Wavelengths of the sound waves
Select all of the following waves that are transverse.
Surface water waves Seismic S waves
Select all of the following functions that could represent a periodic wave on a string initially located on the x-axis that moves up and down in the y direction.
cos sin