Question 93 of 142

A tunning 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 $340{ms}^{-1}$)

Your answerCheck answer

Show answer and solution▾

Answer: 50

We know that, $v=\lambda f$, then, $\lambda =\dfrac{v}{f}=\dfrac{340m{s}^{-1}}{340Hz}=\dfrac{340m{s}^{-1}}{340{s}^{-1}}=1m$
First resonating length, ${l}_{1}=\dfrac{\lambda }{4}=\dfrac{100}{4}=25cm$
Second resonating length, ${l}_{2}=\dfrac{3\lambda }{4}=\dfrac{3\times 100}{4}=75cm$
Third resonating length, ${l}_{3}=\dfrac{5\lambda }{4}=\dfrac{5\times 100}{4}=125cm$
So third resonance is not possible since the length of the tube is $125cm$
Thus, minimum height of water necessary for resonance $=125-75=50cm$