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 $340 \mathrm{~ms}^{-1}$ )
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Solution
Ans. (50)
Sol. Assumption : Ignore word "fundamental mode" in question.
$$
\lambda=\frac{V}{f}=\frac{340}{340}=1 \mathrm{~m}
$$
First resonating length $=\frac{\lambda}{4}=25 \mathrm{~cm}$
Second resonating length $=\frac{3 \lambda}{4}=75 \mathrm{~cm}$
Third resonating length $=\frac{5 \lambda}{4}=125 \mathrm{~cm}$
Height of water required $=125-75=50 \mathrm{~cm}$SOUND WAVE/EASY] [JEE Main 2022] _{S2}_2806
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