JEE Main · 2022 · 28 Jun 2022 · Shift 2 · Waves & Sound

The wavelength of the sound is $\lambda =\frac{v}{f}=\frac{340}{340}=1\text{m}=100$cm. A tube closed at one end resonates when the air-column length is an odd multiple of a quarter wavelength, i.e. at $25,75,125,\dots$ cm, so the initial $125$cm column is the $\frac{5\lambda }{4}$ resonance (despite the wording calling it fundamental). Pouring water shortens the air column, and the next resonance below it is at $\frac{3\lambda }{4}=75$cm. The minimum height of water needed is therefore $125-75=50$cm.