Question

A tuning fork of frequency $340Hz$ resonates in the fundamental mode with an air column of length $125cm$ 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 $340m{s}^{-1}$ )

Answer 1

Answer: 50

Assumption : Ignore word "fundamental mode" in question.
$\lambda =\frac{V}{f}=\frac{340}{340}=1m$
First resonating length $=\frac{\lambda }{4}=25cm$
Second resonating length $=\frac{3\lambda }{4}=75cm$
Third resonating length $=\frac{5\lambda }{4}=125cm$
Height of water required $=125-75=50cm$