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

Question

32. Two loudspeakers, A and B , are driven by the same amplifier and emit sinusoidal waves in phase. Speaker B is 2.00 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 speak- ers emit sound waves that travel directly from the speaker to point Q. (see figure) (a) What is the lowest frequency for which constructive interference occurs at point Q? (b) What is the lowest frequency for which destructive interference occurs at point Q? 2.00 m

William Roberts · Answer

(a)

Constructive interference occurs when the path difference between and n=1,2,3...

Path difference between the points Q of the speakers A andB = 3 m-1 m = 2m

Therefore, n HTML0$ = 2 (or) = (2/n)

We know that Frequency (f), = Velocity(v) / Wavelength(

Velocity of sound waves in air (v), = 344 m/s

Substituting for v in equation (1)

f = (344m/sxn) / 2m = 172Hz xn where n=1,2,3 .....

The lowest frequency at which constructive interference takes place at at the point Q is 172 Hz is the result.

(b)

When the path difference between 32.%20Two%20loudspeakers,%20A%20and%20B%20,%20are%20driven%20by%20the%20same%20amplifier%20and%20emit%20sinusoidal... and n/2 is greater than , destructive interference occurs.

Path difference between the points Q of the speakers A andB = 3 m-1 m = 2m

Thus, n/2x = 2m (or = 4 / n).

Substituting for v in equation (1)

f = (344m/sx n)/ 4m = 86Hz x N where n=1,3,5 .....

Therefore, the lowest frequency at which destructive interference takes place at the point Q is 86 Hz

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