One car while moving towards a cliff, blows a horn with frequency f. If the driver hears an echo of frequency 2f then speed of car in terms of speed of sound is ......

Options

A. (A) v/2`
B. (B)` v/sqrt2`
C. (C) `v/3`
D. (D) `v/4`

Answer

C

Explanation

We have `(f _(L))/( v + v _(L)) = (f _(S))/( v + v ._(S))`
`therefore (2f)/( v + v _(L)) = (f)/( v - v _(L))`
` therefore 2 (v -v _(L)) = v + v _(L)`
`therefore 2v -2v _(L) =v + v _(L)`
`therefore v = 3v_(L)`
`therefore v _(L) = v/3`
Note : In case of an echo, consider an imaginary source on the side opposite to that of real souce with opposite velocity.
Here according to sign convention, velocity in a directon from listner to imaginary source is to be take positive.