The extension in a string,obeying Hooke's law | vedclass

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Question

(A) The speed of a transverse wave in a stretched string is given by $v = \sqrt{\frac{T}{\mu}}$,where $T$ is the tension and $\mu$ is the linear mass

Vedclass · Accepted Answer

$1.22$

Vedclass · Answer

(A) The speed of a transverse wave in a stretched string is given by $v = \sqrt{\frac{T}{\mu}}$,where $T$ is the tension and $\mu$ is the linear mass density.According to Hooke's law,the tension $T$ in the string is proportional to the extension $x$,i.e.,$T = kx$.Therefore,the speed $v$ is proportional to $\sqrt{x}$ (since $\mu$ remains constant),so $v \propto \sqrt{x}$.Given the initial extension is $x$ and speed is $v$,and the new extension is $1.5x$ with new speed $v'$,we have:$\frac{v'}{v} = \sqrt{\frac{1.5x}{x}} = \sqrt{1.5} \approx 1.22$.Thus,the new speed is $v' = 1.22v$.

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 $1.5x$,the speed of sound will be (in $, v$)

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