A source of sound of frequency `256Hz` is moving rapidly towards wall with a velocity of `5m//sec`. How many beats per second will be heard if sound travels at a speed of `330m//sec`.

Explanation

Case-I: When observer is between wall and the source
In this case, the observer is stationary and the source in motion towards observer. The apparent frequency for stationary observer is given by
`n' = n [(v)/(v - v_(s))]`
n = 256 Hz, v = 330 m/s
`v_(s) = 5m/s`
`n' = 256((330)/(330 - 5)) = (256 xx 330)/(325) = 259.93Hz`
In this case, the apparent frequency received by the observer from source is 259.93. The observer also receives the sound reflected from the wall. As reflection does not cause any change in frequency and hence the frequency of reflected sound is also 259.93 Hz.
Thus beats frequency is
`Deltan = 259.93 - 259.93 = 0`
Case-II When the sourcesis between wall and observer
For direct sound, source is moving away from the observer.
`n'' = n((v)/(v+v_(s))) = (330)/(330 + 5) xx 256 = 252.2 Hz`
For reflected sound, source is moving towards wall. Hence
`n' = n((v)/(v - v_(s))) = 259.9`
Thus beat frequency is
`Deltan = n' - n'' = 259.9 - 252.2`
= `7.7 approx 8 Hz`