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A tunning 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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answer is 50.

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Detailed Solution

Assumption : Ignore word “fundamental mode” in question.

$λ = \frac{V}{f} = \frac{340}{340} = 1 m$

First resonating length $= \frac{λ}{4} = 25 cm$

Second resonating length $= \frac{3 λ}{4} = 75 cm$

Third resonating length $= \frac{5 λ}{4} = 125 cm$

Height of water required $= 125 - 75 = 50 cm$

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