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 ..... $f$
JEE MAIN 2016, Medium
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The fundamental frequency in case $(a)$ is $f=\frac{v}{2 \ell}$

The fundamental frequency in case $(b)$ is

$f^{\prime}=\frac{v}{4(\ell / 2)}=\frac{u}{2 \ell}=f$

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