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The extension in a string, obeying Hooke's law, is $x$ . The speed of sound in the stretched string is $v$ . If the extension in the string is increased to $1.5 x,$ the speed of sound will be

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$1 . 22 v$

$1 . 61 v$

$1.50 v$

$0. 75 v$

answer is A.

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Detailed Solution

Given ,

$e_{1} = x$ , $e_{2} = 1.5 x$

Speed $V = \sqrt{\frac{T}{μ}}$

$= \sqrt{\frac{Y A e}{μ l}}$

$V \propto \sqrt{e}$

$\frac{V_{1}}{V_{2}} = \sqrt{\frac{e_{1}}{e_{2}}} = \sqrt{\frac{x}{1.5 x}}$

$\Rightarrow V_{2} = 1.22 V_{1}$

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