Question

A uniform wire of length $L$, diameter $D$ and density $P$ is stretched under a tension $T$. The correct relation between its fundamental frequency $'f'$ , the length $L$ and the diameter $D$ is ............

• A. $f\propto\frac{L}{D^2}$
• B. $f\propto\frac{1}{L D^2}$
• C. $f\propto\frac{1}{LD}$
• D. $f\propto\frac{1}{L\sqrt{D}}$

Answer 1

Answer: (C)

$f\propto\frac{1}{LD}$

Answer 2

The fundamental frequency is
$f=\frac{1}{2 L} \sqrt{\frac{T}{\mu}}$
$f=\frac{1}{2 L} \sqrt{\frac{T}{\rho \pi \frac{D^{2}}{4}}}=\frac{1}{L D} \sqrt{\frac{T}{\pi \rho}}$
$\therefore f \propto \frac{1}{L D}$