Question

Suppose two speakers are arranged such that they emit identical sound waves, and are separated by 4m. A microphone is positioned 3m above one of the speakers. If the speed of sound is 340 m/s, and both speakers start in phase, are turned on at the same time, and emit the same frequency, what is the lowest frequency such that the microphone picks up no sound?

You may ignore amplitude reduction due to distance for this problem.

Answer #1

Pls refer image attached

For no sound to be detected by microphone the two sound waves reaching microphone must interfere destructively

For destructive interference the path difference between two interfering waves must be lamda/2.

Lambda denotes wavelength.

Path difference between waves reaching from 2 sources =S2P-S1P

=5-3

=2m

For destructive interference the path difference between two interfering waves must be lamda/2.

2=(Lambda/2)

Lambda=4

We have the relation v=f(lambda)

v denotes velocity of wave

f denotes frequency of wave

340=f(4)

f=80Hz

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