Question

Average total energy density for a transverse wave is $16\text{J/m}$. The average kinetic energy density for the corresponding wave will be

• A. $4\text{J/m}$
• B. $2\text{J/m}$
• C. $8\text{J/m}$
• D. $16\text{J/m}$

Answer 1

The correct option is C $8\text{J/m}$

Average kinetic energy density is,
$<\frac{dK}{dx}>=\frac{1}{4}\mu A^2{\omega }^2$
Average total energy density is,
$<\frac{dE}{dx}>=<\frac{dK}{dx}>+<\frac{dU}{dx}>$
$\Rightarrow <\frac{dE}{dx}>=\frac{1}{2}\mu A^2{\omega }^2$
Hence, average total energy density is twice that of average kinetic energy density.

$⟨\frac{dE}{dx}⟩=2\times ⟨\frac{dK}{dx}⟩$
$\Rightarrow 16=2\times ⟨\frac{dK}{dx}⟩$
$\Rightarrow ⟨\frac{dK}{dx}⟩=8\text{J/m}$