Question

A string of length $2L$, obeying Hooke's Law, is stretched so that its extension is $L$.The speed of the transverse wave travelling on the string is $v$.If the string is further stretched so that the extension in the string becomes $4L$. The speed of transverse wave travelling on the string will be.

• A. $\sqrt{2v}$
• B. $4\sqrt{2}V$
• C. $2\sqrt{2}V$
• D. $2v$

Answer 1

The correct option is C $2\sqrt{2}V$

we know that,

$\begin{array}{c}V=\sqrt{\frac{T}{\mu }}\\ Now,\\ \frac{V}{V^{{}^{\prime }}}=\sqrt{\frac{T}{\mu }\times \frac{{\mu }_2}{T_2}}=\frac{1}{\sqrt{4\times 2}}\\ or,V^{{}^{\prime }}=2\sqrt{2}V\end{array}$

Hence,

option $C$ is correct answer.