Question

A transverse wave is propagating on a stretched string. The rate of transfer of energy in a wave is

• A. directly proportional to the tension in the string
• B. inversely proportional to the tension in the string
• C. directly proportional to the square root of tension in the string
• D. None of these

Answer 1

The correct option is C directly proportional to the square root of tension in the string

The rate of transfer of energy for a wave is known as power associated with wave.
$P_{\text{avg}}=\frac{1}{2}\mu v{\omega }^2{A}^2$
wave velocity is,
$v=\sqrt{\frac{T}{\mu }}$
where $T=$ Tension in the string.
$\Rightarrow P_{\text{avg}}=\frac{1}{2}\mu \times \sqrt{\frac{T}{\mu }}{\omega }^2{A}^2$
$\Rightarrow P_{\text{avg}}\propto \sqrt{T}$