Question
Asked Nov 8, 2019
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A pair of in-phase stereo speakers is placed side by side, 0.704 m apart. You stand directly in front of one of the speakers, 2.34 m from the speaker.

What is the lowest frequency that will produce constructive interference at your location?

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Expert Answer

Step 1

It is given that the distance between the two speakers arranged side by side is 0.704m and the distance between the person and one of the speakers is 2.34 m . The distance between the person and the other speaker is found by

d 0.704 m
(2.34 m
= 2.44 m
The path difference between the sound waves from the two speakers is found out to be,
path di fference 2.44 m -2.34 m
0.1 m
For constructive interference, the path difference must be an integral multiple of wavelength of
the sound
path difference = nà
Here, n is an integer and A is the wavelength of the sound.
Since it is asked to find the lowest frequency, the value of n will be one. Thus
path di fference = 2
0.1 m
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d 0.704 m (2.34 m = 2.44 m The path difference between the sound waves from the two speakers is found out to be, path di fference 2.44 m -2.34 m 0.1 m For constructive interference, the path difference must be an integral multiple of wavelength of the sound path difference = nà Here, n is an integer and A is the wavelength of the sound. Since it is asked to find the lowest frequency, the value of n will be one. Thus path di fference = 2 0.1 m

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Step 2

The equation for the freq...

f
Here, fis the frequency of the sound and v is the speed of the sound
Speed of the sound in air is 343 m/s
Substitute the numerical values in the above equation.
343 m/s
f
0.1 m
=3430 Hz
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f Here, fis the frequency of the sound and v is the speed of the sound Speed of the sound in air is 343 m/s Substitute the numerical values in the above equation. 343 m/s f 0.1 m =3430 Hz

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