Q)Two loudspeakers, A and B, are driven by the same amplifier as shown 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 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? b) What is the lowest frequency for which destructive interference occurs at point Q? The speed of sound wave is 344 m/s.
Answer:
lowest frequency is 172 Hz. for n = 1
lowest frequency is 86 Hz for n = 0
Explanation:
(a) Constructive interference takes place when the path difference is n where n=1,2,3 ...
frequency f = v /λn
= v n / d
= n ( 344 / 2 )
= n ( 172 ) Hz.
lowest frequency is 172 Hz
b)Destructive interference takes place when the path difference is n/2 x where n=1,3,5 ...
λ = 4/2n+1
for n = 0
λ = 4m
f = 344/4
f = 86 Hz.
lowest frequency is 86 Hz
