Question

A listener is sitting somewhere on the line between two loudspeakers that are 10 m apart. The speakers are each emitting a sine wave with the same frequency and no initial phase difference. The listener finds that the sound is completely cancelled when he is at a distance of 3.5 m from one of the speakers. What is a possible frequency of the sound?

Answer 1

Answer:

57.17 Hz 114.34 Hz 285 Hz

Explanation:

The distance between the men and 1 speaker = 3.5 m

Distance between the men and second speaker = 10-3.5= 6.5 m

Here at this point there will be no sound so there will be destructive interference

Path difference $\Delta x=6.5-3.5=3$

We know that for destructive interference $\Delta x=(2m+1)\frac{\lambda }{2}=(2m+1)\frac{v}{2f}$

$3=(2m+1)\frac{v}{2f}$

$f=(2m+1)\frac{v}{6}$ here v is the speed of sound in air

So for m =0

$f=(2\times 0+1)\frac{343}{6}=57.17H$

for m =1

$f=(2\times 1+1)\frac{343}{6}=114.34Hz$

for m=2

$f=(2\times 2+1)\frac{343}{6}=285Hz$