A guitar string of length $90\,cm$ vibrates with a fundamental frequency of $120\,Hz.$ The length of the string producing a fundamental frequency of $180\,Hz$ will be $...........cm$.
JEE MAIN 2023, Easy
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$f =\frac{ nv }{2 \ell}, \text { for fundamental mode } n =1$
$f =\frac{ v }{2 \ell}$
$f \propto \frac{1}{\ell}$
$\frac{ f _1}{ f _2}=\frac{\ell_2}{\ell_1}$
$\frac{120}{180}=\frac{\ell_2}{90}$
$\ell_2=60\,cm$
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