Two observer `A` and `B` carry identical sound sources of frequency `256 Hz`. If `A` is stationary while `B` moves away from `A` at a speed of `10 m//s`, how many beats per seconds are heard by `A` and `B` ? `(c = 343 m//s)`

Answer

Number of beats `= 7.5 s^(-1)` and `0.725 s^(-1)`

Explanation

For observer `A` , who is stationary, source `B` is moving away at speed `u`.
`v' = (v_(0)C)/(343 - 10) = (343 xx 256)/(353)`
Number of beats `= v_(0)(1 - (343)/(353)) = (256 xx 10)/(353) = 0.725 Hz`.
For oberser `B`,
`v = (v_(0)(C - u_(0)))/(O) = (256 xx 333)/(343)`
Number of beats `= 256 (1 - (333)/(343)) = (256 xx 10)/(343) = 7.46 Hz`.