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. 4 v

Answer 1

The correct option is C

$\sqrt{2}v$

$V\propto \sqrt{T}$

and $T\propto \Delta l$

$\therefore \frac{v_2}{v_1}=\sqrt{\frac{(\Delta l{)}_2}{(\Delta l{)}_1}}$

or $\frac{v_2}{v_1}=\sqrt{\frac{\left(\frac{L}{10}\right)}{\left(\frac{L}{20}\right)}}=\sqrt{2}$

$\therefore v_2=\sqrt{2}v$