The speed of a transverse wave passing… - JEE Main 2022 Physics PYQ

JEE Main 2022 — Physics Waves & Oscillations

2022integermedium

The speed of a transverse wave passing through a string of length $50\mathrm{cm}$ and mass $10g$ is $60m{s}^{-1}$ . The area of cross-section of the wire is $2.0{\mathrm{mm}}^{2}$ and its Young's modulus is $1.2\times {10}^{11}N{m}^{-2}$ . The extension of the wire over its natural length due to its tension will be $x\times {10}^{-5}m$ . The value of $x$ is _____ .

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Held on 29 Jul 2022 · Verified 6 Jul 2026.

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Solution

The wave speed in string is given by ${v}_{w}=\sqrt{\frac{T}{\mu }}$ , where, $T$ is tension and $\mu =\frac{m}{l}$ is linear mass density.

Putting the values, we have

$\Rightarrow 60=\sqrt{\frac{T}{10\times {10}^{-3}}\times 0.5}$

$\Rightarrow T=\frac{{(60)}^{2}\times {10}^{-2}}{0.5}=72N$

The Young's modulus is given by $Y=\frac{Fl}{A\Delta l}$ , here, $A$ is area.

From above the extension of the wire is $\Delta l=\frac{Tl}{AY}=\frac{72\times 0.5}{2\times {10}^{-6}\times 1.2\times {10}^{11}}$ $=\frac{72\times 5}{24}\times {10}^{-5}=15\times {10}^{-5}m$ .

Hence, the value of $x=15$ .

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