Question

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

Answer 1

The driver applies form of frequency $f$.

He nears apparent frequency $f^{\prime }=2f$ after the sound comes reflected from the cliff.

Let velocity of the car (i.e observer) be $u$

In case of reflection where observer moves towards steady wall doppler's formula in given by:

$f^{\prime }=\left(\frac{v+u}{v-u}\right)f$ [$v$ :velocity of sound]

$\Rightarrow 2f=\left(\frac{v+u}{v-u}\right)f$

$\Rightarrow 2v-2u=v+u$

which gives,

$\Rightarrow u=\frac{v}{3}$