A tuning fork of frequency 340 Hz resonates in the fundamental mode… | JEE Main 2022 (28 Jun, Shift 2)

Q78JEE Main 2022 · 28 JUN · SHIFT 2Medium

Organ Pipes & Resonance Tube

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 ${}^{-1}$ )

Numerical answer type. Work it out, then open the answer.

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Answer: 50

$\lambda = \frac{340}{340} = 1$ m, so resonating lengths are $25, 75, 125$ cm.
The 125 cm column is the $\frac{5\lambda}{4}$ resonance; as water is poured the column shortens to the next resonance at 75 cm.
Water height needed $= 125 - 75 = 50$ cm
So the answer is 50 cm.

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