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.

Options

A. `(v+v_m)/(v+v_b)f`
B. `(v+v_m)/(v-v_b)f`
C. `(2v_b(v+v_m))/(v^2-v_b^2) f`
D. `(2v_m(v+v_b))/(v^2-v_m^2) f`

Answer

C

Explanation

The motorist recevies two sound waves direct one and that reflected from the wall.
`f.=(v+v_m)/(v+v_b)f`
For reflected sound waves:
Frequenc of sound wave reflected from the wall is
`f.=f/(v-v_b) times f`

Frequency of the reflected waves as received by the moving motorist is
`f..=(v+v_M)/vtimesf..=(v+v_m)/(v-v_b) times f`
Therefore the beat frequency is
`f..=(v+v_m)/(v-v_b ) timesf-(v+v_m)/(v+v_b) timesf=(2v_b(v+v_m))/(v^2-v_b^2)f`