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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
(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
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