MHT CET · Physics · Waves and Sound

The pitch of the whistle of an engine appears to drop by \(20 \%\) of original value when it passes a stationary observer. If speed of sound in air \(350 \mathrm{~m} / \mathrm{s}\), then speed of engine in \(\mathrm{m} / \mathrm{s}\) is

A \(1050\)
B \(175\)
C \(520.5\)
D \(87.5\)

Verified Solution

Answer & Solution

Correct Answer

(D) \(87.5\)

Step-by-step Solution

Detailed explanation

Aparent pitch heard by the observer \(\mathrm{f}^{\prime}=\frac{4}{5} \mathrm{f}\)
where, \(f\) is the original pitch of the engine.
As the apparent frequency is lowered, thus the engine must be moving away from the stationary observer.
From Doppler effect, apparent frequency heard:
\(\begin{aligned} & \mathrm{f}^{\prime}=\mathrm{f}\left[\frac{\mathrm{V}_{\text {sound }}}{\mathrm{V}_{\text {sound }}+\mathrm{V}_{\text {source }}}\right] \\ & \therefore \frac{4 \mathrm{f}}{5}=\left[\frac{350}{350+\mathrm{V}_{\text {Source }}}\right] \\ & \Rightarrow \mathrm{V}_{\text {Source }}=87.5\end{aligned}\)

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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