First slide

Stationary waves

Question

Fundamental frequency of sonometer wire is n. If the length, tension and diameter of wire are tripled, the new fundamental frequency is

Moderate

A

$\frac{n}{\sqrt{3}}$
B

$\frac{n}{3}$
C

$n \sqrt{3}$
D

$\frac{n}{3 \sqrt{3}}$

Solution

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

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