Q. Fundamental frequency of sonometer wire is $n.$ If the length, tension and diameter of wire are tripled, the new fundamental frequency is
A) $\frac{n}{\sqrt{3}}$
B) $\frac{n}{3}$
C) $n\sqrt{3}$
D) $\frac{n}{3\sqrt{3}}$
Explanation
(d) $n = \frac{1}{2l}\sqrt{\frac{T}{\pi r^{2}\rho}} \Rightarrow n \propto \frac{\sqrt{T}}{lr} \Rightarrow \frac{n_{1}}{n_{2}} = \sqrt{\frac{T_{1}}{T_{2}}} \times \frac{l_{2}}{l_{1}} \times \frac{r_{2}}{r_{1}}$
$= \sqrt{\frac{T}{3T}} \times \frac{3l}{l} \times \frac{3r}{r} = 3\sqrt{3} \Rightarrow n_{2} = \frac{n}{3\sqrt{3}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.