MHT CET · Physics · Waves and Sound

When tension ' \(\mathrm{T}\) ' is applied to a sonometer wire of length ' \(\mathrm{l}\) ' it vibrates with the fundamental frequency ' \(n\) '. Keeping the setup same, when the tension is increased by \(8 \mathrm{~N}\), the fundamental frequency becomes three times the earlier. The initial tension applied to the wire was

A \(2 \mathrm{~N}\)
B \(0.5 \mathrm{~N}\)
C \(0.5 \mathrm{~N}\)
D \(4 N\)

Verified Solution

Answer & Solution

Correct Answer

(B) \(0.5 \mathrm{~N}\)

Step-by-step Solution

Detailed explanation

The initial fundamental frequency of wire can be written as,

On dividing equation ( 2 ) by equation (1), we get
\(\begin{aligned} & 3=\sqrt{\frac{T+8 N}{T}} \\ & \Rightarrow 9 T=T+8 N \\ & \Rightarrow T=1 N\end{aligned}\)

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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