Question

Sinusoidal waves $5.00\text{cm}$ in amplitude are to be transmitted along a string having a linear mass density equal to $4.00\times {10}^{-2}\text{kg/m}$. If the source can deliver a maximum power of $90\text{W}$ and the string is under a tension of $100\text{N}$, then the highest frequency at which the source can operate is (take ${\pi }^2=10$)

• A. 45.3 Hz
• B. 50.0 Hz
• C. 30.0 Hz
• D. 62.3 Hz

Answer 1

The correct option is C 30.0 Hz

$P=\frac{1}{2}\mu {\omega }^2{A}^{2}v$, where

$v=\sqrt{\frac{T}{\mu }}$
$\because f=\omega /2\pi$
$⟹f=\frac{1}{2\pi }\sqrt{\frac{2P}{A^2\sqrt{T\mu }}}$

Using data,
$f=30\text{Hz}$