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 be the speed of the sound, the expression for beat frequency heard by motorist is

Options

A. `(v+v_(m))/(v-v_(b))`
B. `(v+v_(m))/(v-v_(b))`
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

Frequency received by motorist (directly) `f_(1)=f((v+v_(0))/(v+v_(s)))=f((v+v_(m))/(v+v_(b)))`
Frequency received by wall `f.=f((v)/(v-v_(b)))`
Now wall will act as source of frequency f. and motorist as observer.
Second frequency received by motorist `f_(2)=f.((v+v_(m))/(v))=f((v+v_(m))/(v-v_(b)))`
Beat frequency `=f_(2)-f_(1)=(f(v+v_(m))(2v_(b)))/((v^(2)-v_(b)^(2)))`