Physics - Wave on String Question with Solution | TestHub

The fundamental frequency of a stretched wire is given by

$f=\frac{1}{2L}\sqrt{\frac{T}{\mu }}$

where $\mu$ is the mass per unit length of the wire.

The mass per unit length $\mu$ can be written in terms of density $\rho$ and diameter $D$ as

$\mu =\rho \times A=\rho \times \frac{\pi D^2}{4}$

Substituting $\mu$ in the frequency formula, we get

$f=\frac{1}{2L}\sqrt{\frac{T}{\rho \frac{\pi D^2}{4}}}=\frac{1}{2L}\times \frac{2}{D}\sqrt{\frac{T}{\rho \pi }}=\frac{1}{LD}\sqrt{\frac{T}{\rho \pi }}$

For a given tension $T$ and density $\rho$, the fundamental frequency is proportional to

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

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