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

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

Explanation

Frequency received in case `1`
`f_(1) = f((V + V_(m))/(V + V_(b)))`, [using `f' = f((V + V_(m))/(V + V_(b)))`]
and in case `2, f_(2) = f((V + V_(m))/(V - V_(b)))`
Obviously
`f_(2) gt f_(1)`
`:.` Beat frequency `f_(b) = f_(2) - f_(1) = f((V + V_(m))/(V - V_(b))) - f((V + V_(m))/(V + V_(b)))`
or `f_(b) = (2V_(b)(V + V_(m)))/(V^(2) - V_(b^(2)))f`