Question 1

Two in-phase loudspeakers are some distance apart. They emit sound with a frequency of 1536 Hz. You move between the speakers, along the line joining the them, at a constant speed of 2.8 m/s. What beat frequency do you observe? The speed of sound in the room is 330 m/s.

Accepted Answer

The beat frequency is determined by the Doppler effect as you move between the speakers. The frequency shift for each speaker is calculated using the formula: f' = f(v + v0)/v, where f is the original frequency, v is the speed of sound, and v0 is the speed of the observer. The difference in frequency due to the Doppler effect for each speaker results in a beat frequency of approximately 26 Hz.

Question 2

A source emits sound with frequency 1000 Hz. A second source emitting sound simultaneously causes a 4 Hz intensity variation to appear. What are the possible frequencies of the second source?

Accepted Answer

The intensity variation or beat frequency is the absolute difference between the two frequencies. Given a beat frequency of 4 Hz, the second source could be either 996 Hz or 1004 Hz.

Question 3

A 0.640-m long gas column is open at one end and closed at the other. What is the fundamental resonant frequency of the air column if the speed of sound in the air is 340 m/s?

Accepted Answer

The fundamental frequency of a closed-open tube is given by $ f = \frac{v}{4L} $, where $ v $ is the speed of sound and $ L $ is the length of the tube. Substituting the given values, $ f = \frac{340}{4 \times 0.640} = 133 $ Hz.

Question 4

A 1.50-m long gas column that is open at one end and closed at the other has a fundamental resonant frequency 80.0 Hz. What is the sound speed in this gas?

Accepted Answer

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Question 5

If the intensity level of one trombone is 70 dB, what is the intensity level of 76 trombones?

Accepted Answer

The intensity level of multiple sources can be calculated by adding 10log(n), where n is the number of sources. 
So, for 76 trombones, the intensity level would be:
70 + 10log(76) = 89 dB

Question 6

An air column is being designed so that its second lowest resonant frequency is 440 Hz. The column is open at one end and closed at the other. What length should the column be if the speed of sound in air is 340 m/s?

Accepted Answer

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Question 7

A 0.640-m long gas column is open at both ends. What is the fundamental resonant frequency of the air column if the speed of sound in the air is 340 m/s?

Accepted Answer

The fundamental frequency for an open-open tube is given by f = v / (2L), where v is the speed of sound and L is the length of the tube. Substituting the given values, f = 340 / (2 * 0.640) = 266 Hz.

Question 8

A 4.0-m long pipe is closed at one end. Find the frequency of the second harmonic. The speed of sound is 340 m/s.

Accepted Answer

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Question 9

Two microphones, 3.0 m apart, pick up the sound of a source emitting sound at 1024 Hz. The source is moving in a direction parallel to the line joining the microphones. When the source is equidistant from the microphones, the signals picked up by the microphones interfere constructively. At that instant the angle between the right bisector to the line joining the microphones and the line joining the midpoint to the source is 0°. What will the angle be when the two signals again interfere constructively for the first time?The speed of sound is 330 m/s. Assume that the distance to the source of sound is very large compared with the wavelength.

Accepted Answer

The wavelength of the sound is approximately 0.322 m. For constructive interference, the path difference should be an integer multiple of the wavelength. The first constructive interference after the initial one occurs when the path difference is one wavelength. Using geometry and the given conditions, the angle is calculated to be approximately 6.2°.

Question 10

Sound of frequency 600 Hz is emitted by a point source. The sound can travel along two different paths to reach an observer. What is the minimum non-zero path length difference that results in constructive interference? Assume the speed of sound in air is 340 m/s.

Accepted Answer

Constructive interference occurs when the path length difference is a multiple of the wavelength. The wavelength (λ) is calculated by dividing the speed of sound (340 m/s) by the frequency (600 Hz), which gives approximately 0.567 m. The minimum non-zero path length difference for constructive interference is one wavelength, which is 56.7 cm.

Question 11

The sound from a single source can reach point O by two different paths. One path has a length 20.0 m and the second path has a length 21.0 m. The sound destructively interferes at point O. What is the minimum frequency of the source if the speed of sound is 340 m/s?

Accepted Answer

Destructive interference occurs when the path difference is an odd multiple of half wavelengths. The path difference here is 1.0 m. For the first minimum frequency, this path difference equals half a wavelength (λ/2). Therefore, λ = 2 m. Using the speed of sound (v = 340 m/s), frequency (f) is v/λ = 340/2 = 170 Hz.

Question 12

The third harmonic of an organ pipe of length L open at one end has nodes at the closed end, 2L/5 from the closed end, and 4L/5 from the closed end. The open end is an antinode. What expression describes this wave? Take the speed of sound to be 336 m/s, the length of the pipe to be 2.0 m, and let x be the distance from the closed end.

Accepted Answer

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Question 13

A crying baby emits sound with an intensity of 8.0 × 10^-8 W/m². What is the intensity level for a set of quintuplets? The lowest detectable intensity is 1.0 × 10^-12 W/m².

Accepted Answer

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Question 14

Two people are talking at a distance of 3.0 m from where you are and you measure the sound intensity as 1.1 × 10^-7 W/m². Another student is 4.0 m away from the talkers. What sound intensity does the other student measure?

Accepted Answer

The sound intensity decreases with the square of the distance from the source. Using the inverse square law, the intensity at 4.0 m is (3.0/4.0)^2 times the intensity at 3.0 m, which calculates to 6.2 × 10^-8 W/m^2.

Question 15

Two harmonic sound waves reach an observer simultaneously. The observer hears the sound intensity rise and fall with a time of 0.200 s between the maximum intensity and the succeeding minimum intensity. What is the difference in frequency of the two harmonic sound waves?

Accepted Answer

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Question 16

The intensity level of a power mower at a distance of 1.0 m is 100 dB. You wake up one morning to find that four of your neighbors are mowing their lawn 20 m from your open bedroom window. What is the intensity level in your bedroom?

Accepted Answer

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Question 17

A 200-Hz and a 206-Hz sound are emitted into the same volume of space. What is the frequency of intensity variation?

Accepted Answer

The frequency of intensity variation, or beat frequency, is the absolute difference between the two frequencies: |206 Hz - 200 Hz| = 6 Hz.

Question 18

Two tuning forks have frequencies of 480 and 520 Hz. What is the beat frequency if both are emitting a sound at the same time?

Accepted Answer

The beat frequency is the absolute difference between the two frequencies, which is |520 Hz - 480 Hz| = 40 Hz.

Question 19

One of the harmonics of a column of air open at one end and closed at the other has a frequency of 448 Hz and the next higher harmonic has a frequency of 576 Hz. What is the fundamental frequency of the air column?

Accepted Answer

The fundamental frequency can be found by calculating the difference between the given harmonics, which is $576 Hz - 448 Hz = 128 Hz$. Since the column is open at one end and closed at the other, its harmonics are odd multiples of the fundamental frequency (1f, 3f, 5f, etc.). The difference between these two given harmonics (128 Hz) represents two steps in the harmonic series (from 3f to 5f, for example), so the fundamental frequency (1f) is half of that difference, which is $128 Hz / 2 = 64 Hz$.

Question 20

The sound level of a person talking at 1.0 m of distance is 60 dB. You are surrounded by five people all talking at the same time. What sound level are you being exposed to?

Accepted Answer

When multiple sound sources are present, their intensities add up, not their decibel levels. The formula for combining sound levels is: L_total = 10 * log10(10^(L1/10) + 10^(L2/10) + ...). For five people talking at 60 dB each, the combined level is approximately 67 dB.

Quiz 16: Sound