A car is moving towards a high cliff. The driver sounds a horn of frequency f . The reflected sound heard by the driver has frequency 2 f . If v is the velocity of sound, then the velocity of the car, in the same velocity units, will be

Step-by-step solution

1st the car is the source and at the cliff, one observes f ' . ∴   f ' = v v - v s f 2 nd cliff is now source. It emits frequency f ' and the observer is now the driver who observes f '' . ∴   f '' = v + v 0 v f ' or 2 f = v + v 0 v - v s f ⇒   2 v - 2 v 0 = v + v 0 ⇒ v = v 0 + 2 v 0 as  v s = v 0 ⇒   v 0 = v 3