Question

A bullet passes past a person at a speed 220 m/s. The fractional change in the frequency of the whistling sound heard by the person as the bullet crosses the person is (Speed of sound = 330 m/s):

• A. 0.67
• B. 0.8
• C. 1.2
• D. 3

Answer 1

Answer: (B)

0.8

Let the original frequency of the source be $f_o$.
Speed of source $v_{source}=220m/s$
Doppler effect when a source (bullet) moves towards the stationary observer :
Apparent frequency heard $f^{\prime }=f_o[\frac{v_{sound}}{v_{sound}-v_{source}}]$
$\therefore$ $f^{\prime }=f_o[\frac{330}{330-220}]=3f_o$
Doppler effect when a source moves away from the stationary observer :
Apparent frequency heard $f^{\prime \prime }=f_o[\frac{v_{sound}}{v_{sound}+v_{source}}]$
$\therefore$ $f^{\prime \prime }=f_o[\frac{330}{330+220}]=0.6f_o$
Fractional change in frequency $\frac{f^{\prime }-f^{\prime \prime }}{f^{\prime }}=\frac{3f_o-0.6f_o}{3f_o}=0.8$