A tuning fork of frequency $340\,Hz$ resonates in the fundamental mode with an air column of length $125\,cm$ in a cylindrical tube closed at one end. When water is slowly poured in it, the minimum height of water required for observing resonance once again is________ $cm$
(Velocity of sound in air is $340\,ms ^{-1}$ )
JEE MAIN 2022, Diffcult
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Assumption : Ignore word "fundamental mode" in question.
$\lambda=\frac{ V }{ f }=\frac{340}{340}=1\,m$
First resonating length $=\frac{\lambda}{4}=25\,cm$
Second resonating length $=\frac{3 \lambda}{4}=75\,cm$
Third resonating length $=\frac{5 \lambda}{4}=125\,cm$
Height of water required $=125-75=50\,cm$
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