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  4. 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 )

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Q. 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 $340 \,ms ^{-1}$ )

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Solution:

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 $=125-75=50\, cm$