A band playing music at a frequency `f` is moving towards a wall at a speed `v_(b)`. A motorist is following the band with a speed `v_(m)`. If `v` is the speed of sound, obtain an expression for the beat frequency heard by the motorist.

Answer

`(2fv_(b)(v+v_(m)))/((v^(2)-v_(b)^(2)))`

Explanation

Frequency reaching the wall `f_(1)=f_(0)((v)/(v-v_(b)))`
Frequency reaching the motorist after reflection from wall
`f_(1)=f_(1)((v+v_(m))/(v))=f_(0)((v+v_(m))/(v-v_(b)))`
Frequency directly reaching the motorist
`f_(2)=f_(0)((v+v_(m))/(v+v_(b)))`
`:.` Beat frequency
`Deltaf=f_(1)-f_(2)=f_(0)(v+v_(m))((2v)/(v^(2)-v_(b)^(2)))`