Two sources, A and B, emit a sound of a certain wavelength. The sound emitted fr

Question

Two sources, A and B, emit a sound of a certain wavelength. The sound emitted from both sources is detected at a point away from the sources. The sound from source A is a distance d from the observation point, whereas the sound from source B has to travel a distance of 2.7?, where 2.7?<d.

What is the largest value of the wavelength, in terms of d, for the maximum sound intensity to be detected at the observation point?

and

If d=12.7m and the speed of sound is 340.m/s, what is the frequency of the emitted sound?

Explanation / Answer

path difference=d-2.7*lambda

now for constructive interference

d-2.7*lambda=n*lambda

value of n can be 1,2,3....because

d>2.7*lambda

==> d=(n+2.7)*lambda

==> lambda=d/(n+2.7)

so maximum value of lambda when (n+2.7) is minimum +ve

which is for n=1

so lambda= 12.7/3.7

and v=340

==> f=v/lambda=340/(12.7/3.7)=99.05 Hz

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