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  4. In order to double the frequency of the fundamental note emitted by a stretched string, the length is reduced to (3/4) th of the original length and the tension is changed. The factor by which the tension is to be changed is

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Q. 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

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Solution:

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