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_(0))f_(0)`
B. `(v+v_(m))/(v-v_(0))f_(0)`
C. `(2v_(b)(v+v_(m)))/(v^(2)-v_(0)^(2))f`
D. `(2v_(m)(v+v_(b)))/(v^(2)-v_(m)^(2))f`

Answer

A

Explanation

According to Doppler's effect when observer is moving behind the source (band), apparent frequency
heard `n'=n[(v+v_(o))/(v+v_(s))]`
Hence, `v_(o)=v_(m)`
`v_(s)=v_(o)`
`thereforen_(1)=[(v+v_(m))/(v+v_(b))]f`
The reflected sound i.e., echo, reaching the observer from the wall can be regarded as coming from the image of source formed by reflection at the wall this image is approaching the observer in the direction of sound Hence, for reflected sound, frequency heard by motorist
`h_(2)=f_(o)[(v+v_(o))/(v+v_(s))]`
or `h_(2)=f_(o)[(v+v_(m))/(v+v_(o))]`