Question

For a transverse wave
Statement $1$ : Total average energy density is the sum of average $\text{K.E.}$ density and average $\text{P.E.}$ density

Statement $2$ : Average $\text{K.E.}$ density is equal to the average $\text{P.E.}$ density

• A. Statement $1$ is correct and Statement $2$ is incorrect.
• B. Statement $2$ is correct and Statement $1$ is incorrect.
• C. Both the statements are correct.
• D. Both the statements are incorrect.

Answer 1

The correct option is C Both the statements are correct.

We know,
Total energy density $=\text{Avg. K.E + Avg . P.E}$
$⟨\frac{dE}{dx}⟩=⟨\frac{dK}{dx}⟩+⟨\frac{dU}{dx}⟩$
$\text{Total energy density}=\frac{1}{4}\mu {\omega }^2{A}^2+\frac{1}{4}\mu {\omega }^2{A}^2$
$\therefore \text{Total energy density}=\frac{1}{2}\mu {\omega }^2{A}^2$
$\Rightarrow$ Both the statements are correct.