First slide

Stationary waves

Question

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

Moderate

A

n
B

$\frac{n}{\sqrt{2}}$
C

$\frac{n}{2}$
D

$\frac{n}{2 \sqrt{2}}$

Solution

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

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