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 ......

One car while moving towards a cliff, blows a horn with frequency f. I

1.	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 ......
Answer» (A) V/2` (B)` v/sqrt2` (C) `v/3` (D) `v/4` Solution : 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.