Question

A string of length $L$ is stretched by $L/20$ and speed of transverse wave along it is $v.$ The speed of wave When it is stretched by $L/10$ will be (assume that Hooke's law is applicable)

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

Answer 1

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

$\begin{array}{c}v=\text{velocity of wave}\\ k=\text{constant of propertionality}\end{array}$

$\begin{array}{c}\text{Using,}v\propto \sqrt{\Delta l}\\ \begin{array}{cc}{v}_1& =k\sqrt{\frac{L}{20}}=v\\ v_2& =k\sqrt{\frac{2L}{20}}=v\sqrt{2}\\ \text{Ans}& =\left(C\right)\end{array}\end{array}$