Question

A string of length $L$ is stretched by $\frac{L}{20}$ and speed of transverse wave 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)

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

Answer 1

The correct option is C

$\sqrt{2}v$

$V\alpha \sqrt{T}$

And $T\alpha \Delta /$

$\therefore -\frac{V_2}{V_1}=\sqrt{\frac{(\Delta /{)}_2}{(\Delta /{)}_1}}$

Or $\frac{V_2}{V}=\sqrt{\frac{\left(L/10\right)}{\left(L/20\right)}}=\sqrt{2}$

$V_2=\sqrt{2}V$