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Q. Two identical strings $X$ and $Z$ made of same material have tension $T _{ X }$ and $T _{ Z }$ in them. It their fundamental frequencies are $450 Hz$ and $300 \,Hz ,$ respectively, then the ratio $T _{ x } / T _{7}$, is :

JEE MainJEE Main 2020Waves

Solution:

$f =\frac{1}{2 \ell} \sqrt{\frac{ T }{\mu}}$
For identical string $l$ and $\mu$ will be same
$f \propto \sqrt{ T }$
$\frac{450}{300}=\sqrt{\frac{ T _{ x }}{ T _{ y }}}$
$\frac{ T _{ x }}{ T _{ y }}=\frac{9}{4}=2.25$