Q. If the tension and diameter of a sonometer wire of fundamental frequency $n$ are doubled and density is halved then its fundamental frequency will become
A) $\frac{n}{4}$
B) $\sqrt{2}n$
C) $n$
D) $\frac{n}{\sqrt{2}}$
Explanation
(c) $n = \frac{1}{2l}\sqrt{\frac{T}{\pi r^{2}\rho}} \propto \sqrt{\frac{T}{r^{2}\rho}}$
$\Rightarrow \frac{n_{1}}{n_{2}} = \sqrt{\left( \frac{T_{1}}{T_{2}} \right)\left( \frac{r_{2}}{r_{1}} \right)^{2}\left( \frac{\rho_{2}}{\rho_{1}} \right)} = \sqrt{\left( \frac{1}{2} \right)\left( \frac{2}{1} \right)^{2}\left( \frac{1}{2} \right)} = 1$
$\therefore n_{1} = n_{2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.