Question: A sound source of frequency 500 Hz and an observer are moving along their line of motions with speed...

Question

A sound source of frequency 500 Hz and an observer are moving along their line of motions with speeds 10 m/s and 20 m/s respectively. The frequency of the sound as heard by the observer at the moment as shown in the figure is nearly equal to (speed of sound in air is 340 m/s):

Answer 1

Solution

Along the joining line, components of velocities are towards each other. Hence effect of motions of both is to increase apparent frequency. Thus apparent frequency is

f = 500 $\left| \frac{340 + 20\cos 53^{o}}{340 - 10\cos 37^{o}} \right|$ = 530 Hz