The length of the string of a musical instrument is $90 \;cm$ and has a fundamental frequency of $120 \;Hz$. Where (In $cm$) should it be pressed to produce fundamental frequency of $180 \;Hz ?$
NEET 2020, Medium
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Frequency of stretched string
$n =\frac{1}{2 \ell} \sqrt{\frac{ T }{ m }}$
If $T$ and $m$ are constant
$n \propto \frac{1}{\ell}$
$\frac{ n ^{\prime}}{ n }=\frac{\ell}{\ell^{\prime}}$
$\frac{180}{120}=\frac{90}{\ell}$
$\ell=60 cm$
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