Question:
A source of sound $S$ emitting waves of frequency $100\, Hz$ and an observor $O$ are located at some distance from each other. The source is moving with a speed of $19.4\, m s^{-1}$ at an angle of $60^{\circ}$ with the source observer line as shown in the figure. The observor is at rest. The apparent frequency observed by the observer is (velocity of sound in air $330\, ms ^{-1}$ )
A source of sound $S$ emitting waves of frequency $100\, Hz$ and an observor $O$ are located at some distance from each other. The source is moving with a speed of $19.4\, m s^{-1}$ at an angle of $60^{\circ}$ with the source observer line as shown in the figure. The observor is at rest. The apparent frequency observed by the observer is (velocity of sound in air $330\, ms ^{-1}$ )
Updated On: Dec 17, 2025
- 103 Hz
- 106 Hz
- 97 Hz
- 100 Hz
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The Correct Option is A
Solution and Explanation
Here, original frequency of sound, $f_{0}=100 \,Hz$
Speed of source $V_{s} 19.4 \cos 60^{\circ}=9.7$
From Doppler's formula
$f^{1}=f_{0}\left(\frac{V-V_0}{V-V_{s}}\right)$
$f^{1}=100\left(\frac{V-0}{V-(+9.7)}\right)$
$f^{1} 100 \frac{V}{V\left(1-\frac{9.7}{V}\right)}$ $f^{1}=100\left(1+\frac{9.7}{330}\right)=103 \,Hz$
Apparent frequency $f^{1}=103 \,Hz$
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Concepts Used:
Doppler Effect
The Doppler effect is a phenomenon caused by a moving wave source that causes an apparent upward shift in frequency for observers who are approaching the source and a visible downward change in frequency for observers who are retreating from the source. It's crucial to note that the impact isn't caused by a change in the source's frequency.
The Doppler effect may be seen in any wave type, including water waves, sound waves, and light waves. We are most familiar with the Doppler effect because of our encounters with sound waves