Question 1

For a diffraction horn loudspeaker,sound emerges through a rectangular opening.The opening of a diffraction horn has a width of 0.12 m.If the speaker emits a continuous tone with a wavelength of 0.09 m,at what angle does the first minimum occur?
A)47°
B)39°
C)23°
D)12°
E)66°

Accepted Answer

E

Question 2

Two loudspeakers,A and B,are separated by a distance of 2.0 m.The speakers emit sound waves at a frequency of 680 Hz that are exactly out of phase.The speed of sound is 343 m/s.How far from speaker A along the +x axis will a point of constructive interference occur? 
A)0.25 m
B)0.30 m
C)0.46 m
D)0.88 m
E)0.98 m

Accepted Answer

D

Question 3

Consider the figures depicting rectangular pulses on a string.

-Which pulses must be superimposed to give the situation shown in 5.
A)1 and 2
B)1 and 3
C)2 and 4
D)1,2,and 4
E)2,3,and 4.

Accepted Answer

B

Question 4

For a diffraction horn loudspeaker,the sound emerges through a rectangular opening.The width of a diffraction horn is 0.14 m.If the speed of sound in air is 343 m/s,at what frequency is the diffraction angle  equal to 35°?
A)3300 Hz
B)4300 Hz
C)6300 Hz
D)7700 Hz
E)9200 Hz

Accepted Answer

The diffraction angle can be calculated using the formula:
θ = λ/wavelength

where θ is the diffraction angle, λ is the wavelength, and w is the width of the opening.

We can rearrange the formula to solve for the frequency:
λ = w/tan(θ)
λ = 0.14 m / tan(35°)
λ = 0.0977 m

The wavelength and speed of sound can be used to calculate the frequency:
v = fλ
343 m/s = f(0.0977 m)
f = 3511 Hz

The closest answer choice is B) 4300 Hz.

Question 5

Water waves approach an aperture.The resulting patterns are shown for two different cases,A and B,in which the wavelength and aperture size are varied.  Which one of the following statements concerning these cases is true?
A)Neither figure shows diffraction.In both cases,the wavelength is much smaller than the aperture.
B)Diffraction occurs in A,but not in B because the wavelength in A is much smaller than the aperture.
C)Diffraction occurs in B,but not in A because the wavelength in B is much smaller than the aperture.
D)Both figures show diffraction.In both cases,the wavelengths are approximately the same size as the aperture.
E)Diffraction occurs in B,but not in A because the wavelength in B is approximately the same size as the aperture.

Accepted Answer

The answer of Water waves approach an aperture.The resulting patterns...

Question 6

Two timpani (tunable drums)are played at the same time.One is correctly tuned so that when it is struck,sound is produced that has a wavelength of 2.20 m.The second produces sound with a wavelength of 2.10 m.If the speed of sound is 343 m/s,what beat frequency is heard?
A)7 beats/s
B)9 beats/s
C)11 beats/s
D)13 beats/s
E)15 beats/s

Accepted Answer

The beat frequency is calculated by finding the difference between the frequencies of the two sounds. First, calculate the frequencies of both sounds using the formula $f = v/\lambda$, where $v$ is the speed of sound and $\lambda$ is the wavelength. For the first timpani, $f_1 = 343 \, \text{m/s} / 2.20 \, \text{m} = 155.91 \, \text{Hz}$, and for the second, $f_2 = 343 \, \text{m/s} / 2.10 \, \text{m} = 163.33 \, \text{Hz}$. The beat frequency is the absolute difference between these two frequencies: $|f_2 - f_1| = |163.33 \, \text{Hz} - 155.91 \, \text{Hz}| = 7.42 \, \text{Hz}$, which rounds to approximately 7 beats/s.

Question 7

Which one of the following superpositions will result in beats?
A)the superposition of waves that travel with different speeds
B)the superposition of identical waves that travel in the same direction
C)the superposition of identical waves that travel in opposite directions
D)the superposition of waves that are identical except for slightly different amplitudes
E)the superposition of waves that are identical except for slightly different frequencies

Accepted Answer

Beats occur when two waves of slightly different frequencies are superposed. The resulting wave will have a varying amplitude (i.e. amplitude modulation) at a frequency equal to the difference between the two original frequencies. Therefore, choice E is the best one.

Question 8

Two loudspeakers are located 3.0 m apart on the stage of an auditorium.  A listener at point P is seated 19.0 m from one speaker and 15.0 m from the other.  A signal generator drives the speakers in phase with the same amplitude and frequency.  The wave amplitude at P due to each speaker alone is A.  The frequency is then varied between 30 Hz and 400 Hz.  The speed of sound is 343 m/s.
-Determine the value of the maximum amplitude in terms of A.
A)2.0A
B)2.5A
C)3.0A
D)4.0A
E)5.0A

Accepted Answer

The maximum amplitude occurs when the waves from the two speakers arrive at point P in phase, which means they constructively interfere. Constructive interference happens when the path difference between the waves is an integer multiple of the wavelength, leading to a phase difference of $2\pi n$ (where $n$ is an integer). The amplitude of the resultant wave at point P is the sum of the amplitudes of the individual waves, which is $A + A = 2A$ in this case, since the problem states that the wave amplitude at P due to each speaker alone is $A$.

Question 9

Two pulses of identical shape travel toward each other in opposite directions on a string,as shown in the drawing.Which one of the following statements concerning this situation is true? 
A)The pulses will reflect from each other.
B)The pulses will diffract from each other.
C)The pulses will interfere to produce a standing wave.
D)The pulses will pass through each other and produce beats.
E)As the pulses pass through each other,they will interfere destructively.

Accepted Answer

The answer of Two pulses of identical shape travel toward...

Question 10

Two loudspeakers are located 3.0 m apart on the stage of an auditorium.  A listener at point P is seated 19.0 m from one speaker and 15.0 m from the other.  A signal generator drives the speakers in phase with the same amplitude and frequency.  The wave amplitude at P due to each speaker alone is A.  The frequency is then varied between 30 Hz and 400 Hz.  The speed of sound is 343 m/s.
-At what frequency or frequencies will the listener at P hear a maximum intensity?
A)170 Hz only
B)113 Hz and 226 Hz
C)86 Hz,170 Hz,257,and 343 Hz
D)57 Hz,114 Hz,171 Hz,228 Hz,285,342,and 399 Hz
E)43 Hz,85 Hz,128 Hz,170 Hz,213 Hz,257 Hz,298,344,and 387 Hz

Accepted Answer

The answer of Two loudspeakers are located 3.0 m apart...

Question 11

Two identical tuning forks vibrate at 587 Hz.After a small piece of clay is placed on one of them,eight beats per second are heard.What is the period of the tuning fork that holds the clay? A)1.68 × 10^-³ s B)1.70 × 10^-³ s C)1.73 × 10^-³ s D)1.76 × 10^-³ s E)1.80 × 10^-³ s

Accepted Answer

The frequency of the tuning fork with the clay is either 587 Hz + 8 Hz = 595 Hz or 587 Hz - 8 Hz = 579 Hz. The period $T$ is given by $T = \frac{1}{f}$. For 595 Hz, $T = \frac{1}{595} \approx 1.68 \times 10^{-3} s$, and for 579 Hz, $T = \frac{1}{579} \approx 1.73 \times 10^{-3} s$. Since 1.68 × 10^-3 s corresponds to the unaltered tuning fork and 1.73 × 10^-3 s to the one with clay (because adding clay lowers the frequency), the correct answer is 1.73 × 10^-3 s.

Question 12

A speaker is designed for wide dispersion for a high frequency sound.What should the diameter of the circular opening be for a speaker where the desired diffraction angle is 11° and a 9100 Hz sound is generated? The speed of sound is 343 m/s.
A)0.039 m
B)0.077 m
C)0.24 m
D)0.13 m
E)0.048 m

Accepted Answer

The answer of A speaker is designed for wide dispersion...

Question 13

Two traveling pulses on a rope move toward each other at a speed of 1.0 m/s.The waves have the same amplitude.The drawing shows the position of the waves at time t = 0 s.Which one of the following drawings depicts the waves on the rope at t = 2.0 s?  
A)a
B)b
C)c
D)d
E)e

Accepted Answer

The answer of Two traveling pulses on a rope move...

Question 14

A guitar string has a linear density of 8.30 × 10^-⁴ kg/m and a length of 0.660 m.The tension in the string is 56.7 N.When the fundamental frequency of the string is sounded with a 196.0-Hz tuning fork,what beat frequency is heard? A)6 Hz B)4 Hz C)12 Hz D)8 Hz E)2 Hz

Accepted Answer

The fundamental frequency of the string can be calculated using the formula $f = \frac{1}{2L} \sqrt{\frac{T}{\mu}}$, where $L$ is the length of the string, $T$ is the tension in the string, and $\mu$ is the linear density of the string. Substituting the given values: $f = \frac{1}{2 \times 0.660} \sqrt{\frac{56.7}{8.30 \times 10^{-4}}}$, calculating this gives $f \approx 194 \, \text{Hz}$. The beat frequency is the absolute difference between the frequencies of the tuning fork and the string, which is $|196 - 194| = 2 \, \text{Hz}$. Therefore, there was an error in the initial selection; the correct answer is E, not D.

Question 15

A speaker generates a continuous tone of 440 Hz.In the drawing,sound travels into a tube that splits into two segments,one longer than the other.The sound waves recombine before being detected by a microphone.The speed of sound in air is 339 m/s.What is the minimum difference in the lengths of the two paths for sound travel if the waves arrive exactly out of phase at the microphone? 
A)0.10 m
B)0.39 m
C)0.77 m
D)1.11 m
E)1.54 m

Accepted Answer

When the sound waves recombine at the microphone, if they are out of phase, they will interfere destructively, resulting in no sound being detected. For a continuous tone of 440 Hz, the period is T = 1/f = 1/440 seconds. If the path length difference is equal to half the wavelength, λ/2, the waves will arrive exactly out of phase. The wavelength of the sound wave is given by λ = v/f = 339/440 m. Therefore, the path length difference should be:

ΔL = λ/2 = (339/440)/2 = 0.385 m

This means that the longer path should be 0.385 m longer than the shorter path to cause destructive interference. The closest value to this is option B) 0.39 m.

Question 16

A guitar string produces 4 beats/s when sounded with a 250 Hz tuning fork and 9 beats per second when sounded with a 255 Hz tuning fork.What is the vibrational frequency of the string?
A)240 Hz
B)246 Hz
C)254 Hz
D)259 Hz
E)263 Hz

Accepted Answer

The difference between the frequencies of the tuning forks is 255 Hz - 250 Hz = 5 Hz. Since the string produces 4 beats per second with the 250 Hz tuning fork and 9 beats per second with the 255 Hz tuning fork, the frequency of the string must be somewhere in between these two values.

One way to find the frequency of the string is to take the average of these two values, which is (250 Hz + 255 Hz)/2 = 252.5 Hz. However, another approach is to find the frequency that produces a difference of 5 beats per second, which would correspond to half of a wavelength of the string.

Thus, the frequency of the string can be calculated as follows:

frequency of string = average of tuning fork frequencies ± (beats per second/2)
frequency of string = 252.5 Hz ± (5 beats/s)/2
frequency of string = 252.5 Hz ± 2.5 Hz
frequency of string = 250 Hz or 255 Hz

Since the beats are more frequent with the 255 Hz tuning fork, it is likely that the frequency of the string is closer to 255 Hz than 250 Hz. Therefore, the best choice is B) 246 Hz.

Question 17

Consider the figures depicting rectangular pulses on a string.

-Complete the following statement: If pulse 2 were superimposed on pulse 3,
A)constructive interference would occur.
B)the resulting pattern would be represented by 1.
C)the resulting pattern would be represented by 4.
D)the resulting pattern would be represented by 5.
E)the resulting pattern would be different than 1,4,and 5.

Accepted Answer

The answer of Consider the figures depicting rectangular pulses on...

Question 18

A pebble is dropped in a lake;and it produces ripples with a frequency of 0.50 Hz.When should a second pebble be dropped at the same place to produce destructive interference?
A)0.50 s after the first
B)0.75 s after the first
C)1.0 s after the first
D)1.5 s after the first
E)2.0 s after the first

Accepted Answer

Destructive interference occurs when two waves are out of phase by 180 degrees, which corresponds to half a wavelength or half a period in time. Given the frequency of 0.50 Hz, the period (T) is the reciprocal of the frequency, T = 1/f = 1/0.50 Hz = 2.0 s. Half of this period is 1.0 s, so dropping the second pebble 1.0 s after the first will result in destructive interference.

Question 19

Sound waves are emitted from two speakers.Which one of the following statements about sound wave interference is false?
A)In a region where both destructive and constructive interference occur,energy is not conserved.
B)Destructive interference occurs when two waves are exactly out of phase when they meet.
C)Interference redistributes the energy carried by the individual waves.
D)Constructive interference occurs when two waves are exactly in phase when they meet.
E)Sound waves undergo diffraction as they exit each speaker.

Accepted Answer

Energy is always conserved in wave interference. Destructive interference results in a decrease in amplitude (and thus energy) compared to the individual waves, but this is compensated by constructive interference leading to an increase in amplitude (and energy) in other regions. Therefore, statement A is false.

Question 20

Consider the figures depicting rectangular pulses on a string.

-If pulse 1 were reflected from a wall,which one of the patterns above would represent the reflected pulse?
A)1
B)2
C)3
D)4
E)5

Accepted Answer

The answer of Consider the figures depicting rectangular pulses on...

Quiz 17: The Principle of Linear Superposition and Interference Phenomena

For a diffraction horn loudspeaker,sound emerges through a rectangular opening.The opening of a diffraction horn has a width of 0.12 m.If the speaker emits a continuous tone with a wavelength of 0.09 m,at what angle does the first minimum occur?

Two loudspeakers,A and B,are separated by a distance of 2.0 m.The speakers emit sound waves at a frequency of 680 Hz that are exactly out of phase.The speed of sound is 343 m/s.How far from speaker A along the +x axis will a point of constructive interference occur?

Consider the figures depicting rectangular pulses on a string. -Which pulses must be superimposed to give the situation shown in 5.

Two timpani (tunable drums) are played at the same time.One is correctly tuned so that when it is struck,sound is produced that has a wavelength of 2.20 m.The second produces sound with a wavelength of 2.10 m.If the speed of sound is 343 m/s,what beat frequency is heard?

Which one of the following superpositions will result in beats?

Two identical tuning forks vibrate at 587 Hz.After a small piece of clay is placed on one of them,eight beats per second are heard.What is the period of the tuning fork that holds the clay?

A speaker is designed for wide dispersion for a high frequency sound.What should the diameter of the circular opening be for a speaker where the desired diffraction angle is 11° and a 9100 Hz sound is generated? The speed of sound is 343 m/s.

Two traveling pulses on a rope move toward each other at a speed of 1.0 m/s.The waves have the same amplitude.The drawing shows the position of the waves at time t = 0 s.Which one of the following drawings depicts the waves on the rope at t = 2.0 s?

A guitar string has a linear density of 8.30 × 10^-⁴ kg/m and a length of 0.660 m.The tension in the string is 56.7 N.When the fundamental frequency of the string is sounded with a 196.0-Hz tuning fork,what beat frequency is heard?

A guitar string produces 4 beats/s when sounded with a 250 Hz tuning fork and 9 beats per second when sounded with a 255 Hz tuning fork.What is the vibrational frequency of the string?

Consider the figures depicting rectangular pulses on a string. -Complete the following statement: If pulse 2 were superimposed on pulse 3,

A pebble is dropped in a lake;and it produces ripples with a frequency of 0.50 Hz.When should a second pebble be dropped at the same place to produce destructive interference?

Sound waves are emitted from two speakers.Which one of the following statements about sound wave interference is false?

Consider the figures depicting rectangular pulses on a string. -If pulse 1 were reflected from a wall,which one of the patterns above would represent the reflected pulse?

Quiz 17: The Principle of Linear Superposition and Interference Phenomena

For a diffraction horn loudspeaker,sound emerges through a rectangular opening.The opening of a diffraction horn has a width of 0.12 m.If the speaker emits a continuous tone with a wavelength of 0.09 m,at what angle does the first minimum occur?

Two loudspeakers,A and B,are separated by a distance of 2.0 m.The speakers emit sound waves at a frequency of 680 Hz that are exactly out of phase.The speed of sound is 343 m/s.How far from speaker A along the +x axis will a point of constructive interference occur?

Consider the figures depicting rectangular pulses on a string. -Which pulses must be superimposed to give the situation shown in 5.

For a diffraction horn loudspeaker,the sound emerges through a rectangular opening.The width of a diffraction horn is 0.14 m.If the speed of sound in air is 343 m/s,at what frequency is the diffraction angle equal to 35°?

Water waves approach an aperture.The resulting patterns are shown for two different cases,A and B,in which the wavelength and aperture size are varied. Which one of the following statements concerning these cases is true?

Two timpani (tunable drums) are played at the same time.One is correctly tuned so that when it is struck,sound is produced that has a wavelength of 2.20 m.The second produces sound with a wavelength of 2.10 m.If the speed of sound is 343 m/s,what beat frequency is heard?

Which one of the following superpositions will result in beats?

Two pulses of identical shape travel toward each other in opposite directions on a string,as shown in the drawing.Which one of the following statements concerning this situation is true?

Two identical tuning forks vibrate at 587 Hz.After a small piece of clay is placed on one of them,eight beats per second are heard.What is the period of the tuning fork that holds the clay?

A speaker is designed for wide dispersion for a high frequency sound.What should the diameter of the circular opening be for a speaker where the desired diffraction angle is 11° and a 9100 Hz sound is generated? The speed of sound is 343 m/s.

Two traveling pulses on a rope move toward each other at a speed of 1.0 m/s.The waves have the same amplitude.The drawing shows the position of the waves at time t = 0 s.Which one of the following drawings depicts the waves on the rope at t = 2.0 s?

A guitar string has a linear density of 8.30 × 10-⁴ kg/m and a length of 0.660 m.The tension in the string is 56.7 N.When the fundamental frequency of the string is sounded with a 196.0-Hz tuning fork,what beat frequency is heard?

A guitar string produces 4 beats/s when sounded with a 250 Hz tuning fork and 9 beats per second when sounded with a 255 Hz tuning fork.What is the vibrational frequency of the string?

Consider the figures depicting rectangular pulses on a string. -Complete the following statement: If pulse 2 were superimposed on pulse 3,

A pebble is dropped in a lake;and it produces ripples with a frequency of 0.50 Hz.When should a second pebble be dropped at the same place to produce destructive interference?

Sound waves are emitted from two speakers.Which one of the following statements about sound wave interference is false?

Consider the figures depicting rectangular pulses on a string. -If pulse 1 were reflected from a wall,which one of the patterns above would represent the reflected pulse?

A guitar string has a linear density of 8.30 × 10^-⁴ kg/m and a length of 0.660 m.The tension in the string is 56.7 N.When the fundamental frequency of the string is sounded with a 196.0-Hz tuning fork,what beat frequency is heard?