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 $v_s$ = 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 $\left(f_1\right)$ before crossing the bullet is given by:

$f_1=\left(\frac{v}{v-v_s}\right)\times f$

On substituting the values, we get:
$f_1=\left(\frac{330}{330-220}\right)\times f=3f....\left(1\right)$

Apparent frequency heard by the person $\left(f_2\right)$ after crossing the bullet is given by:

$f_2=\left(\frac{v}{v+v_s}\right)\times f$

On substituting the values, we get:
$f_2=\left(\frac{330}{330+220}\right)\times f=0.6f.....\left(2\right)$
So,
$\left(\frac{f_2}{f_1}\right)=\frac{0.6f}{3f}=0.2$

∴ Fractional change = 1 − 0.2 = 0.8