A \( 3.6 \mathrm{~m} \) long pipe resonates with a source of frequency \( 212.5 \mathrm{~Hz} \) ...

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A \( 3.6 \mathrm{~m} \) long pipe resonates with a source of frequency \( 212.5 \mathrm{~Hz} \) when water level is at certain heights in the pipe. Find the heights of water level (from the bottom of the pipe) at which resonances occur. Neglect end correction. Now the pipe is filled to a height \( H(\approx 3.6 \mathrm{~m}) \). A small hole is drilled
\( P \) very close to its bottom and water is allowed to leak. Obtain

W an expression for the rate of fall of water level in the pipe as a function of \( H \). If the radii of the pipe and the hole are \( 2 \times 10^{-2} \mathrm{~m} \) and \( 1 \times 10^{-3} \mathrm{~m} \) respectively. Calculate the time interval between the occurrence of first two resonances. Speed of sound in air is \( 340 \mathrm{~m} / \mathrm{s} \) and \( g=10 \mathrm{~m} / \mathrm{s}^{2}(2000,10 \mathrm{M}) \)
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