JEE MAIN - Physics (2016 (Offline) - No. 15)
A pipe open at both ends has a fundamental frequency $$f$$ in air. The pipe is dipped vertically in water so that half of it is in water. The fundamental frequency of the air column is now :
$$2f$$
$$f$$
$${f \over 2}$$
$${3f \over 4}$$
Explanation
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The fundamental frequency in case $$(a)$$ is $$f = {v \over {2\ell }}$$
The fundamental frequency in case $$(b)$$ is
$$f'{v \over {4\left( {\ell /2} \right)}} = {u \over {2\ell }} = f$$
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