Question 1

When two sound waves are out of phase by _____, destructive interference will occur.

Accepted Answer

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Question 2

Of the frequencies listed below, to which one is the human ear most sensitive?

Accepted Answer

The human ear is most sensitive to frequencies between 2,000 Hz and 5,000 Hz, with the peak sensitivity being around 3,300 Hz. Therefore, choice C is the best answer as it falls within this range.

Question 3

If the distance between a point sound source and a dB detector is increased by a factor of 10, what will be the reduction in intensity level?

Accepted Answer

According to the inverse square law, as the distance between the point sound source and dB detector is increased by a factor of 10, the intensity level will decrease by a factor of 100 (i.e. 10 squared). This corresponds to a reduction of 20 dB, as each 10-fold decrease in intensity level corresponds to a reduction of 10 dB. Therefore, the correct answer is option C.

Question 4

What sound level change most nearly corresponds to a factor of three change in intensity?

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Question 5

If I₀ = 10 ^- ¹² W/m² is the threshold of hearing, a sound with intensity I₁ = 10 ^- ¹⁰ W/m² will give a certain decibel level. Suppose a new sound has an intensity I₂ = I₁²/I₀. What is the new decibel level?

Accepted Answer

The decibel level is calculated using the formula 10 * log10(I/I0). For I1, the decibel level is 20 dB. For I2 = I1^2/I0, the decibel level is 10 * log10((I1^2/I0)/I0) = 10 * log10(I1^2/I0^2) = 2 * 10 * log10(I1/I0) = 2 * 20 = 40 dB.

Question 6

A phase difference of 480° corresponds to what wavelength difference?

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Question 7

If one-half of the members of a symphony orchestra are absent because of head colds, thus reducing the overall intensity of sound by 50%, what will be the reduction in the decibel level?

Accepted Answer

A reduction in sound intensity by 50% corresponds to a 3 dB reduction in decibel level. This is because the decibel scale is logarithmic, with a decrease in intensity of 50% corresponding to a decrease of approximately 3 dB.

Question 8

If the intensity of a sound is increased by a factor of 1000, how is the decibel level changed? The new decibel level will be:

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Question 9

By what amount does the sound intensity decrease when the distance to the source triples?

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Question 10

The intensity level of sound 30 m from a jet airliner is 120 dB. At what distance from the airplane will the sound intensity level be a tolerable 100 dB? (Assume spherical spreading of sound.)

Accepted Answer

The inverse square law for sound states that the sound intensity level decreases by 6 dB for every doubling of the distance from the source. 
To decrease the sound intensity level from 120 dB to 100 dB, we need to decrease it by 20 dB. 
20 dB / 6 dB per doubling = 3.33 doublings of distance 
2^3.33 = 10.6 
So the distance from the airplane must be multiplied by 10.6 to decrease the intensity level by 20 dB. 
30 m x 10.6 = 318 m, which is closest to choice C, 300 m.

Question 11

A source of sound has an intensity  and when its sound level is measured at a fixed distance the value found is 70 dB. The source then has its intensity increased to  and when its sound level is measured at the same distance the value found is 96 dB. What is the ratio  ?

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Question 12

Two loudspeakers are placed facing each other and driven by the same source at 680 Hz. A listener is positioned between the two speakers on the line separating them, thus creating a constructive interference at the listener's ear. What minimum distance would one of the speakers be moved back away from the listener to produce destructive interference at the listener's ear? (The speed of sound = 340 m/s.)

Accepted Answer

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Question 13

If the air temperature decreases, how does the resonant frequency in a pipe closed at one end change?

Accepted Answer

The speed of sound in air decreases with a decrease in temperature, which in turn decreases the resonant frequency in a pipe closed at one end.

Question 14

A very loud train whistle has an acoustic power output of 80 W. If the sound energy spreads out spherically, what is the intensity level in dB at a distance of 100 meters from the train? (I₀ = 10 ^- ¹²W/m²)

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Question 15

The air in a pipe resonates at 150 Hz and 750 Hz, one of these resonances being the fundamental. If the pipe is open at both ends, how many resonances are between the two given ones, and if the pipe is closed at one end, how many resonances are between the two given ones?

Accepted Answer

For an open pipe, the resonant frequencies are given by f = n*v/2L, where n is an integer, v is the speed of sound, and L is the length of the pipe. The given frequencies correspond to n=1 and n=3. The number of resonances between them is therefore 3-1=2.
For a closed pipe, the resonant frequencies are given by f = n*v/4L, where n is an odd integer. The given frequencies correspond to n=3 and n=7. The number of resonances between them is therefore (7-3)/2=2/2=1.

Question 16

What is the intensity of a sound with a measured intensity level of 84 dB? (I₀ = 10^-¹² W/m²)

Accepted Answer

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Question 17

Doubling the distance between sound source and a listener will change the intensity, as detected by the listener, by what factor?

Accepted Answer

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Question 18

A sound intensity of 70 dB is observed at a distance d from the source of sound. What sound intensity would be observed at a distance 2d from the source?

Accepted Answer

Sound intensity decreases with distance from the source according to the inverse square law. This means that at a distance of 2d, the sound intensity will be reduced to 1/4 (or 6 dB lower) of the original intensity at distance d.

Using the formula I2 = I1/(d2/d1)², where I1 is the initial intensity, d1 is the initial distance, I2 is the final intensity, and d2 is the final distance, we can calculate the new sound intensity:

I2 = 70 dB / (2/1)²
I2 = 70 dB / 4
I2 = 17.5 dB

Taking into account that the decrease in intensity is 6 dB, we can subtract this from the initial intensity of 70 dB to obtain:

I2 = 70 dB - 6 dB
I2 = 64 dB

Therefore, the new sound intensity observed at a distance of 2d from the source is 64 dB.

Question 19

What is the intensity of sound from a band with a sound level of 120 dB? (I₀ = 10 ^- ¹² W/m²)

Accepted Answer

The intensity level in decibels (dB) is given by the formula: L = 10 * log10(I/I0). For 120 dB, I = I0 * 10^(120/10) = 10^(-12) * 10^12 = 1 W/m^2.

Question 20

In the afternoon, the decibel level of a busy freeway is 80 dB with 100 cars passing a given point every minute. Late at night, the traffic flow is only 8 cars per minute. What is the late-night decibel level?

Accepted Answer

The decibel level is logarithmic, meaning it decreases by 3 dB for every halving of the number of cars passing. Therefore, if the traffic flow is 100 cars per minute during the day and 8 cars per minute at night, the difference is a reduction of about 12 halvings (100 divided by 8 is approximately 12.5). This gives a total reduction of about 36 dB (12 halvings times 3 dB per halving). Thus, the late-night decibel level is 80 dB minus 36 dB, which equals 44 dB. However, this is an unrealistic answer, as even a completely quiet environment has a decibel level above 0. Therefore, it is safe to assume that the actual late-night decibel level is higher than 0 dB, but significantly lower than 80 dB. Among the given choices, D (69 dB) seems to be the closest estimate, although it is still somewhat arbitrary.

Quiz 13: Sound