devarshi-dt-logo

Question:

A stationary source emits sound of frequency f0=492Hz. The sound is reflected by a large car approaching the source with a speed of 2m/s. The reflected signal is received by the source and superposed with the original. What will be the beat frequency of the resulting signal in Hz?

Solution:

Given f0=492Hz, vcar=2m/s, and vsound=330m/s
Now apparent frequency heard by person in the car is
f1 = f0 * (vsound + vcar) / vsound = (330+2)/330 * 492
Apparent frequency received by source is
f2 = f1 * vsound / (vsound - vcar) = 492 * 332/330 * 330 / (330 - 2) = 498Hz
Now beat frequency b = |f2 - f1| = 498 - 492 = 6Hz