Question

A source of ultrasonic wave is emitting ultrasonic waves of frequency 30 kHz. It is placed in a moving car. With what velocity is the car moving If the frequency appears to be 20 kHz to a stationary observer? Velocity of sound in car 340 ms^-1.

Answer 1

Here the listener is at rest and the source is moving. As the apparent frequency is lesser than the actual frequency, the source is moving away from the listener. 

To find the velocity with the source is moving: 

The apparent frequency is given by,

Here,f' is the apparent frequency = 20 kHz

f is the actual frequency = 30 kHz

v is the velocity of sound = 340 ms^-1

On substituting the values, \(\frac{20}{30}\) = \(\frac{340}{340 + v_s}\)

cross multiplying, 2(340 + v_S) = 3 × 340 2 × 340 + 2v_s = 3 × 340

2 . v_s = 3 × 340 – (2 × 340) or 2 . v_s = 340

v_s = \(\frac{340}{2}\) = 170ms^-1

∴ The car is moving with a velocity of 170ms^-1 away from the listener.