MHT CET · Physics · Waves and Sound

A wire of length ' \(L\) ' and linear density ' \(m\) ' is stretched between two rigid supports with tension ' \(T\) '. It is observed that wire resonates in the \(\mathrm{P}^{\mathrm{th}}\) harmonic at a frequency of 320 Hz and resonates again at next higher frequency of 400 Hz . The value of ' \(p\) ' is

A 2
B 4
C 8
D 10

Verified Solution

Answer & Solution

Correct Answer

(B) 4

Step-by-step Solution

Detailed explanation

\(\begin{aligned} & 320=\frac{\mathrm{p}}{2 l} \sqrt{\frac{\mathrm{~F}}{\mu}} \text { and } 400=\frac{\mathrm{p}+1}{2 l} \sqrt{\frac{\mathrm{~F}}{\mu}} \\ & \frac{400}{320}=\frac{\mathrm{p}+1}{\mathrm{p}} \Rightarrow 400 \mathrm{p}=320 \mathrm{p}+320 \\ & \mathrm{p}=4\end{aligned}\)

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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