Physics - Wave on String Question with Solution | TestHub

Given, Frequency $=f$, Diameter $=D$, Length $=L$, Density $=\rho$ and Tension $=T$ Now, we know that $f=\frac{c}{\lambda }$, $\therefore f=\frac{1}{2L}\times \sqrt{\frac{T}{\mu }}$ where $\mu$ is mass per unit length And mass per unit length is related to density via, $\mu =\left(\pi \times \frac{D^2}{4}\right)\frac{1}{\rho }$ So, the frequency is $f=\frac{1}{2L}\times \sqrt{\frac{T}{\left(\frac{\pi D^2}{4\rho }\right)}}$ $\therefore f\propto \frac{1}{LD}$