A source of sonic oscillations with frequency `n=1700Hz` and a receiver are located on the same normal to a wall. Both the source and receiver are stationary, and the wall recedes from the source with velocity `u=6.0(m)/(s)`. Find the beat frequency registered by the receiver. The velocity of sound is `v=340(m)/(s)`.

Explanation

As both source and receiver are at rest, the frequency of sound waves which directly reach receiver will be 1700 Hz and the frequency of sound which the wall will receive as a moving observer is
`n_1=n_0[(v)/(v+u)]`
The wall now behaves as a moving source of frequency `n_1` which when received by receiver, the ferquency observed is
`n_2=n_1[(v-u)/(v)]=n_0((v-u)/(v+u))`
`=1700[(340-0.06)/(340+0.06)]`
`=1700xx(339.94)/(340.06)=1699.4Hz`
Thus beat frequency received by detector is `trianglen=1700-1699.4=0.6Hz`.