A source of sonic oscillations with frequency `v_(0)=100Hz` moves at right angles to the wall with a velocity `u=0.17 m//s`. Two stationary receivers `R_(1)` and `R_(2)` are located on a straight line, coinciding with the trajectory of the source , in the following succession :` R_(1)-` source `-R_(2)-` wall. Which receiver registers the beatings and what is the beat frequency ? The velocity of sound is equal to `upsilon= 340 m//s`.

Explanation

Receiver `R_(1)` registers the beating , due to the sound waves reaching directly to it from source and the other due to the reflection from the wall.
Frequency of sound reaching directly from `S` to `R_(1)`
`v_(S rarrR_(1))= v_(0)(v)/(vv-u)` when `S` moves towards `R_(1)` and `v'_(S rarr R_(1))=v_(0)(v)/( v+u)` when `S` moves towards the wall Now frequency reaching to `R_(1)` after reflection from wall
`v_(WrarrR_(1))=v_(0)(v)/( u+u)`, when `S` moves towards `R_(1)` and `v'_(WrarrR_(1))=v_(0)(v)/(v-u)`, when `S` moves towards the wall
Thus the souht beta frequency
`Delta v=(v_(SrarrR_(1))-v_(WrarrR_(1)))` or `(v'_(WrarrR_(1))-v_(SrarrR_(1)))`
`=v_(0)(v)/(v-u)-v_(0)(v)/(v+u)=(2 v_(0)vu)/(v^(2)-u^(2))~=(2uv_(0))/(v)=1Hz`