Question

If the amplitude of a transverse wave is doubled then average rate of transmission of potential energy becomes

• A. one fourth of initial value
• B. twice of its initial value
• C. four times of its initial value
• D. none of these

Answer 1

The correct option is C four times of its initial value

We know that
Average rate of transmission of potential energy is,
$<\frac{dU}{dt}>=\frac{1}{4}\mu v{\omega }^2{A}^2$
$\Rightarrow <\frac{d{U}^{\prime }}{dt}>=\frac{1}{4}\mu v{\omega }^2{A}^{\prime 2}$
Given: $A^{\prime }=2A$
$\Rightarrow <\frac{d{U}^{\prime }}{dt}>=\frac{1}{4}\mu v{\omega }^2(2A{)}^2$
$\Rightarrow <\frac{d{U}^{\prime }}{dt}>=4\left(\frac{1}{4}\mu v{\omega }^2{A}^2\right)$
$\therefore <\frac{d{U}^{\prime }}{dt}>=4<\frac{dU}{dt}>$
Hence average rate of transmission of potential energy becomes $4\text{times}$ of its initial value.