Question

Kinetic energy $\left(\text{in joule}\right)$ in one wave length of transverse wave is twice of its average kinetic energy per unit length The wave length of the transverse wave is

• A. $0.2\text{m}$
• B. $2\text{m}$
• C. $3\text{m}$
• D. $4\text{m}$

Answer 1

The correct option is B $2\text{m}$

K.E associated with one wave length of a transverse wave is,
$\Rightarrow K_{\lambda }=\frac{1}{4}\lambda \mu {\omega }^2{A}^2$
Avg. K.E per unit length of string,
$\Rightarrow K_{\text{Avg}}=\frac{1}{4}\mu {\omega }^2{A}^2$
Given,
$K_{\lambda }=2K_{\text{Avg}}$
$\Rightarrow \frac{1}{4}\lambda \mu {\omega }^2{A}^2=2\left(\frac{1}{4}\mu {\omega }^2{A}^2\right)$
$\Rightarrow \lambda =2\text{m}$