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A string of length 'L' is stretched by $\frac{L}{20}$ and the speed of transverse waves along it is 'v'. The speed of wave when it is stretched by $\frac{L}{10}$ will be (assume that Hooke's law is applicable)

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$\frac{v}{\sqrt{2}}$

$v \sqrt{2}$

answer is C.

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Detailed Solution

The tension in the string is proportional to the strain in the string.

So the tension is proportional to the change in length of the string.

$\Rightarrow \frac{v_{1}}{v_{2}} = \sqrt{\frac{∆ x_{1}}{∆ x_{2}}} \Rightarrow v_{2} = v \sqrt{2}$

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