Question

The frequency of the sound heard by the motorcyclist is given by the expression
A motorcyclist moves to the left with a speed of 20 m/s. A police car with velocity 30 m/s to the right emits a sound with a
frequency of 400 Hz. Speed of sound in air is 340 m/s.

Answer 1

Answer:

464.52 Hz

Explanation:

This is a Doppler effect, the Doppler effect causes a change in frequency when the source of the wave is moving or the listener is moving. The general equation is given by:

$f'=f(\frac{v\pm v_d}{v\pm v_s} )$

Where f is the frequency of the source = 400 Hz, v is Speed of sound in air = 340 m/s, vd is the velocity of the observer = 20 m/s and vs is the velocity of the source = 30 m/s

Since the observer is moving towards the source, the numerator is v + vd. The source is also moving towards the observer therefore the denominator is v - vs.

The frequency of the sound heard by the motorcyclist (f') is given by the expression:

$f'=f(\frac{v\pm v_d}{v\pm v_s} )\\f'=f(\frac{v+ v_d}{v- v_s} )=400(\frac{340+20}{340-30})=464.52\ Hz$