Two loudspeakers, A and B , are driven by the same amplifier and emit sinusoidal

Question

Two loudspeakers, A and B, are driven by the same amplifier and emit sinusoidal waves in phase. Speaker B is d = 1.80 m to the right of speaker A. Consider point Q along the extension of the line connecting the speakers, 1.00 m to the right of speaker B. Both speakers emit sound waves that travel directly from the speaker to point Q.

(a) What is the lowest frequency for which constructive interference occurs at point Q?
Hz

(b) What is the lowest frequency for which destructive interference occurs at point Q?
Hz

Explanation / Answer

a) lambda = 1.8 m

f = v/lambda

f = 343/1.8 = 190.6 Hz

b) for distructive

For destructive interference, the path difference must be n + 1/2 wavelengths. The lowest frequency for this would be the longest wavelength, with the path difference equal to one-half wavelength

lambda = 2*1.8 = 3.6 m

f = 343/3.6 = 95.28 Hz

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