Question

A transverse wave having amplitude $A$ and angular frequency $\omega$ is travelling on a string of linear mass density $\mu$. If amplitude is doubled and angular frequency is halved, average kinetic energy per unit length will be

• A. Doubled
• B. Remain same
• C. Halved
• D. None of these.

Answer 1

The correct option is B Remain same

Average kinetic energy per unit length is,
$<\frac{dK}{dx}>=\frac{1}{4}\mu {\omega }^2{A}^2$
Given: ${\omega }^{\prime }=\frac{\omega }{2}$ and $A^{\prime }=2A$
Therefore new average kinetic energy per unit length is,
$\Rightarrow <\frac{d{K}^{\prime }}{dx}>=\frac{1}{4}\mu {\left(\frac{\omega }{2}\right)}^2(2A{)}^2$
$\Rightarrow <\frac{d{K}^{\prime }}{dx}>=\frac{1}{4}\mu {\omega }^2{A}^2$
$\therefore$ option $\left(b\right)$ is correct.