Question

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. $\frac{n}{2 \sqrt{3}}$
• C. $n \sqrt{3}$
• D. $\frac{n}{3 \sqrt{3}}$

Answer 1

Answer: (D)

$n=\frac{1}{2 l} \sqrt{\frac{T}{\pi r^{2} \rho}}$
$\Rightarrow n \propto \frac{\sqrt{T}}{l r}$
$\Rightarrow \frac{n_{1}}{n_{2}}=\sqrt{\frac{T_{1}}{T_{2}}} \times \frac{l_{2}}{l_{1}} \times \frac{r_{2}}{r_{1}}$
$=\sqrt{\frac{T}{3 T}} \times \frac{3 l}{l} \times \frac{2 r}{r}=3 \sqrt{3}$
$\Rightarrow n_{2}=\frac{n}{3 \sqrt{3}}$