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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 - Physics

Sum

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.

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Solution

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
Concept: Speed of Wave Motion
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APPEARS IN

HC Verma Class 11, 12 Concepts of Physics 1
Chapter 16 Sound Waves
Q 67 | Page 356
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