First slide

Stationary waves

Question

In order to double the frequency of the fundamental note emitted by a stretched string, the length is reduced to $\frac{3}{4} th$ of the original length and the tension is changed. The factor by which the tension is to be changed, is

Moderate

A

$\frac{3}{8}$
B

$\frac{2}{3}$
C

$\frac{8}{9}$
D

$\frac{9}{4}$

Solution

$n = \frac{1}{2 l} \sqrt{\frac{T}{m}} \Rightarrow n \propto \frac{\sqrt{T}}{l}$
$\Rightarrow \frac{T_{2}}{T_{1}} = {(\frac{n_{2}}{n_{1}})}^{2} {(\frac{l_{2}}{l_{1}})}^{2} = {(2)}^{2} {(\frac{3}{4})}^{2} = \frac{9}{4}$

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