Question

If potential energy density is twice the average rate of transmission of potential energy. The speed of transverse wave is

• A. $0.5\text{m/s}$
• B. $2\text{m/s}$
• C. $5\text{m/s}$
• D. $1\text{m/s}$

Answer 1

The correct option is A $0.5\text{m/s}$

Potential energy density is the potential energy per unit length of string,
$<\frac{dU}{dx}>=\frac{1}{4}\mu {\omega }^2{A}^2$
Avg. rate of transmission of potential energy is,
$<\frac{dU}{dt}>=\frac{1}{4}\mu v{\omega }^2{A}^2$
Given:
$<\frac{dU}{dx}>=2<\frac{dU}{dt}>$
$\Rightarrow \frac{1}{4}\mu {\omega }^2{A}^2=2\times \frac{1}{4}\mu v{\omega }^2{A}^2$
$\Rightarrow v=\frac{1}{2}=0.5\text{m/s}$