Physics - Wave on String Question with Solution | TestHub

Fundamental frequency of a vibrating string is expressed as $$f=\frac{1}{2L}\sqrt{\frac{T}{\mu }}=\frac{1}{LD}\sqrt{\frac{T}{\pi \rho }}$$ where, $$\begin{array}{rl}& D=\text{ diameter of string }\\ & \rho =\text{ density of the }\\ & \text{ material of string }\end{array}$$ As length $L$ and radius are doubled, the new frequency $$f^{\prime }=\frac{1}{(2L)(2D)}\sqrt{\frac{T}{\pi \rho }}=\frac{1}{4}f$$