Q. A uniform wire of length L, diameter D and density S is stretched under a tension T. the correct relation between its fundamental frequency f, the length L and the diameter D is
A) $f \propto \frac{1}{LD}$
B) $f \propto \frac{1}{L\sqrt{D}}$
C) $f \propto \frac{1}{D^{2}}$
D) $f \propto \frac{1}{LD^{2}}$
Explanation
(a) The fundamental frequency is
$f = \frac{1}{2L} = \sqrt{\frac{T}{\mu}}$
$f = \frac{1}{2L} = \sqrt{\frac{T}{\rho\pi\frac{d^{2}}{4}}} = \frac{1}{LD}\sqrt{\frac{T}{\pi\rho}}$
$\therefore f \propto \frac{1}{LD}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.