In order to double the frequency of the fundamental note emitted … - Vidyadip

MCQ

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

A
$\frac{3}{8}$
B
$\frac{2}{3}$
C
$\frac{8}{9}$
✓
$\frac{9}{4}$

✓

Answer

Correct option: D.

$\frac{9}{4}$

(d)$n=\frac{1}{2 l} \sqrt{\frac{T}{m}}$
$ \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$
$=(2)^2\left(\frac{3}{4}\right)^2=\frac{9}{4}$

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