A driver is riding a car with velocity `v_c` between two vertical walls on a horizontal surface as shown in figure.A source of sound of frequency 'f' is situated on the car. (`v_c lt lt v`, where v is the speed of sound in air )

Beat frequency observed by the driver corresponding to sound waves reflected from wall-1 amd wall-2 (reflected waves corresponding to waves directly coming from source ):

Options

A. `v_c/v f`
B. `(2v_c)/v f`
C. `v_c/(2v) f`
D. `(4v_c)/v f`

Explanation

`f_(1l)=f_(1r)=v/(v-v_c)f, f_(2l)=f_(2r)=v/(v+v_c)f`
Now, for driver `f_(dr1)=(v+v_c)/vf_(1r)`
and `f_(dr2)=(v+v_c)/v f_(2r)`
So, beat frequency =`|f_(dr1)-f_(dr2)|`
`=|(v+v_c)/v f_(1r)-(v-v_c)/v f_(2r)|={((v+v_c)^2-(v-v_c)^2)/((v+v_c)(v-v_c))}f`
`=((4w_c)/v^2)f=((4w_c)/v)f`