Question

A bullet passes past a person at a speed of 220 m s−1. Find the fractional change in the frequency of the whistling sound heard by the person as the bullet crosses the person. Speed of sound in air = 330 m s−1.

Answer 1

Given:

Velocity of bullet vs = 220 ms−1

Speed of sound in air v = 330 ms−1

Let the frequency of the bullet be f.

Apparent frequency heard by the person (f1) before crossing the bullet is given by:

 f1=(vv−vs)×f

On substituting the values, we get:

f1=(330330−220)×f=3f  ....(1)

Apparent frequency heard by the person (f2) after crossing the bullet is given by:

f2=(vv+vs)×f

On substituting the values, we get:

 f2=(330330+220)×f=0.6f   .....(2) 

So,

 (f2f1)=0.6f3f=0.2

∴ Fractional change = 1 − 0.2 = 0.8