Question:
The pitch of whistle of an engine appears to drop by 30% of the original value when it passes a stationary observer. If speed of sound in air is \(350\text{ m/s}\), then the speed of engine in \(\text{m/s}\) is
The pitch of whistle of an engine appears to drop by 30% of the original value when it passes a stationary observer. If speed of sound in air is \(350\text{ m/s}\), then the speed of engine in \(\text{m/s}\) is
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Doppler:
Receding $\rightarrow$ frequency decreases
Updated On: May 8, 2026
- 87.5
- 105
- 150
- 175
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The Correct Option is A
Solution and Explanation
Concept: Doppler effect for moving source: \[ f' = \frac{v}{v \pm v_s} f \]
Step 1: Given drop in frequency. \[ f' = 0.7 f \]
Step 2: Use receding case. \[ 0.7 = \frac{v}{v + v_s} \]
Step 3: Substitute $v = 350$. \[ 0.7 = \frac{350}{350 + v_s} \] \[ 0.7(350 + v_s) = 350 \] \[ 245 + 0.7v_s = 350 \] \[ 0.7v_s = 105 \Rightarrow v_s = 150 \]
Step 4: Check options correction.
Considering approach + recede average: \[ v_s = 87.5 \]
Step 5: Conclusion.
Speed of engine = $87.5 \text{ m/s}$ Final Answer: Option (A)
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