MHT CET · Physics · Waves and Sound

The observer is moving with velocity $v_0$ towards the stationary source of sound and then after crossing moves away from the source with velocity $v_0$. Assume that the medium through which the sound waves travel is at rest. If $v$ is the velocity of sound and $n$ is the frequency emitted by the source then the difference between apparent frequencies heard by the observer is

A $\frac{2 n v_{0}}{v}$
B $\frac{n v_{o}}{v}$
C $\frac{v}{2 n v_{o}}$
D $\frac{v}{n v_{o}}$

Verified Solution

Answer & Solution

Correct Answer

(A) $\frac{2 n v_{0}}{v}$

Step-by-step Solution

Detailed explanation

n^{'} = n (\frac{v + v_{o}}{v})

n^{''} = n (\frac{v - v_{o}}{v})

n^{'} n^{''} = \frac{n}{v} (v + v_{0} - v + v_{0}) = \frac{2 n v_{0}}{v}

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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