A sonometer wire of resonating length 90 cm has a fundamental frequency of 400 Hz when kept under some tension. The resonating length of the wire with fundamental frequency of 600 Hz under same tension ________ cm.

JEE Mains · Physics · STD 11 - Waves and sound

A sonometer wire of resonating length \(90 \mathrm{~cm}\) has a fundamental frequency of \(400 \mathrm{~Hz}\) when kept under some tension. The resonating length of the wire with fundamental frequency of \(600 \mathrm{~Hz}\) under same tension ________ \(\mathrm{cm}\).

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Verified Solution

Correct Answer

(D) \(60\)

Detailed explanation

\(\mathrm{f}_0=400 \mathrm{~Hz} ; \mathrm{v}=\sqrt{\frac{\mathrm{T}}{\mu}}=\text { constant }\)

\(\frac{\lambda}{2}=\mathrm{L} ; \mathrm{v}=\mathrm{f}_0 \lambda\)

\(\frac{\mathrm{v}}{2 \mathrm{f}_0}=\mathrm{L} \Rightarrow \mathrm{v}=2 \mathrm{Lf}_0\)

\(\mathrm{~L}^{\prime}=\frac{\mathrm{v}}{2 \mathrm{f}^{\prime}}=\frac{2 \mathrm{Lf}_0}{2 \mathrm{f}^{\prime}}\)

\(=\frac{L f_0}{\mathrm{f}^{\prime}}=\frac{90 \times 400}{600}=60\)

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