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

`((2V_b(V+V_m)f)/((v^(2)-V_b^(2))))`
Required beat frequency `=| f_1-f_2|`
Where, `f_1=` apparent frequency for the motorist corresponding to the singles directly coming to him from source, and `f_2=` apparent frequency for the motorist corresponding to the signals coming to him after reflection.
Now, `f_1=f[(V+V_m)/(V+V_b)] f_2=(V+V_m)/(V-V_b)`
Hence,the beat frequency `=|f_1-f_2|=(2V_0(V+V_m)f)/((V^(2)-V_b^(2)))`