Question

A person standing on a road sends a sound signal to the driver of a car going away from him at a speed of 72 km h⁻¹. The signal travelling at 330 m s⁻¹ in air and having a frequency of 1600 Hz gets reflected from the body of the car and returns. Find the frequency of the reflected signal as heard by the person.

Answer 1

Given:
Velocity of sound in air v = 330 ms⁻¹
Frequency of signal emitted by the source $n_0$ = 1600 Hz

Velocity of source v_s = 72 kmh⁻¹ = $72\times \frac{5}{18}=20{\mathrm{ms}}^{-1}$

As the sound gets reflected, therefore:

Velocity of source ( v_s ) = Velocity of observer ( v_L )

Velocity of sound heard by the observer is given by:

$n=\frac{v+v_L}{v-v_s}\times n_0$

On substituting the values, we get:

$n=\frac{330-20}{330+20}\times 1600=1417\mathrm{Hz}$

The frequency of the reflected signal as heard by the person is 1417 Hz.