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.

Explanation

Actual frequency of band music is f. The direct frequency heard by motorist is
`f_1=(v+v_m)/(v-v_b)f` ..(i)
The frequency heard by observer at wall is
`f'=(v)/(v-v_0)f`
The reflection does not cause any change in frequency therefore, frequency `f'` is reflected as such and the motorist is approaching the wall. Hence the frequency of reflected sound heard by motorist is
`f_2=(v+v_m)/(v)f'`
`=(v+v_m)/(v)xx(v)/(v-v_b)f=(v+v_m)/(v-v_b)f`
`=((v+v_b)-(v-v_b))/(v^2-v_b^2)(v+v_m)f`
`x=(2v_b(v+v_m)f)/(v^2-v_b^2)`