A siren emitting a sound of frequency 1000 Hz moves away from you towards a cliff at a speed of 10 m/s. (a) What is the frequency of the sound you hear coming directly from the siren ? (b) What is the frequency of the sound you hear reflected off the cliff (c) What beat frequency would you hear ? Take the speed of sound in air as, 330 m/s.

Explanation

The situation is as shown in figure.

(a) Frequency of sound reaching directly to us (by S)
`f_(1)=f((V)/(V-V_(S)))f=((330)/(330+10))(1000)`
(b) Frequency of sound which is reflected of from the cliff is same as that received by cliff (treating cliff as a stationary observer)
`f_(2)=f((V)/(V-V_(s)))f=((330)/(330-10))(1000)`
`=1031.3Hz`.
(c) Beat frequency `=f_(2)-f_(1)=60.7Hz`
So, Beat frequency heard is zero.