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Q.
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 :-
$\frac{ n _1}{ n _2}=\frac{\frac{ v _1}{4 \ell}}{\frac{ v _2}{4 \ell}}$
$\frac{400}{ n _2}=\frac{ v _1}{ v _2}[$ from $v \propto \sqrt{ T }]$
$\frac{400}{ n _2}=\sqrt{\frac{ T _1}{ T _2}}$
$\frac{400}{ n _2}=\sqrt{\frac{300}{363}}$
$\Rightarrow n _2=440 \,Hz$