Q. The fundamental frequency of a sonometre wire is $n.$ If its radius is doubled and its tension becomes half, the material of the wire remains same, the new fundamental frequency will be
A) $n$
B) $\frac{n}{\sqrt{2}}$
C) $\frac{n}{2}$
D) $\frac{n}{2\sqrt{2}}$
Explanation
(d) $n = \frac{1}{2l}\sqrt{\frac{T}{\pi r^{2}\rho}} \Rightarrow n \propto \frac{\sqrt{T}}{r}$
$\Rightarrow \frac{n_{2}}{n_{1}} = \frac{r_{1}}{r_{2}}\sqrt{\frac{T_{2}}{T_{1}}} = \frac{1}{2} \times \sqrt{\frac{1}{2}} = \frac{1}{2\sqrt{2}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.