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

57.17 Hz 114.34 Hz 285 Hz

Step-by-step 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)(\lambda )/(2)=(2m+1)(v)/(2f)`

`3=(2m+1)(v)/(2f)`

`f=(2m+1)(v)/(6)` here v is the speed of sound in air

So for m =0

`f=(2* 0+1)(343)/(6)=57.17H`

for m =1

`f=(2* 1+1)(343)/(6)=114.34Hz`

for m=2

`f=(2* 2+1)(343)/(6)=285Hz`