Question

A rocket is moving at a speed of 220 m^-1 towards a stationary target. While moving, it emits a wave of frequency 1200 Hz. Some of the sound reaching the target gets reflected back to the rocket as an echo. Calculate (i) the frequency of the sound as detected by the target and (ii) the frequency of the echo as detected by the rocket

(velocity of sound = 330 m/s)

Answer 1

Given: v_s = 220 m/s, v_L = 0 m/s, n = 1200 Hz

To find: Apparent frequency (n)

Calculation: For first case, observer is stationary and source i.e., rocket is moving towards the target.

Hence, using formula (i),

frequency of sound as detected by the target,

n = 1200 \((\frac{330}{330-220})\) = 3600 Hz

For second case, target acts as a source with frequency 3600 Hz as it is the source of echo.

While rocket detector acts as an observer. This means, v_s = 0 and V_L = 220 m/s

Using formula (ii),

frequency of echo as detected by the rocket,

n = 3600 \((\frac{330+220}{330})\) = 600 Hz