In the figure, two identical loudspeakers, A and B, driven by the same amplifier

Question

In the figure, two identical loudspeakers, A and B, driven by the same amplifier, are separated by 2.00 m and produce sound waves of the same frequency. A small microphone is placed at point C, 2.9 m from speaker A along the line perpendicular to the line connecting the two speakers. At this point destructive interference occurs. If the microphone is now moved along this line to point D, 4.8 m from speaker A, constructive interference occurs. Find the frequency of the sound waves. The speed of sound is 344 m/s. Assume that there are no other points between C and D where interference occurs.

Explanation / Answer

let,

r1=2 m

r2=2.9 m

r2'=4.8 m

at point C path diffrence is

p.d=sqrt(r1^2+r2^2)-r2

=sqrt(2^2+2.9^2)-2.9

=0.623 m

at point D path diffrence is

p.d'=sqrt(r1^2+r2^2)-r2

=sqrt(2^2+4.8^2)-4.8

=0.4 m

now,

p.d-pd'=lambda/2

0.623-0.4=lambda/2

===>wavelength, lambda=0.446 m

frquency, f=v/lambda

f=344/0.446

===>

frequency, f=771.3 Hz

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