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

Answer: (C)

$\sqrt{2}v$

Answer 2

Dl₁ = $\frac{L}{20}$, Dl₂ = $\frac{L}{10}$

$\begin{matrix} v \propto \sqrt{T} \end{matrix}$ and as stress µ strain

T µ Dl

$\frac { \mathrm { v } ^ { \prime } } { \mathrm { v } } = \sqrt { \frac { \Delta \ell _ { 2 } } { \Delta \ell _ { 1 } } }$ $\begin{matrix} v' = \sqrt{2}v \end{matrix}$