An organ pipe filled with a gas at $27^{\circ}\,C$ resonates at $400\,Hz$ in its fundamental mode. If it is filled with the same gas at $90^{\circ}\,C$, the resonance frequency at the same mode will be $...........\,Hz$
NEET 2022, Medium
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$\frac{ n _1}{ n _2}=\frac{\frac{ v _1}{4 \ell}}{\frac{ v _2}{4 \ell}}$
$\frac{400}{ n _2}=\frac{ v _1}{ v _2}[\text { from } v \propto \sqrt{ T }]$
$\frac{400}{ n _2}=\sqrt{\frac{ T _1}{ T _2}}$
$\frac{400}{ n _2}=\sqrt{\frac{300}{363}}$
$\Rightarrow n _2=440\,Hz$
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