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  4. A cylindrical tube, open at both ends, has a fundamental frequency in air. The tube is dipped vertically in water so that half of its length is in water. The fundamental frequency of the air column is now

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Q. A cylindrical tube, open at both ends, has a fundamental frequency in air. The tube is dipped vertically in water so that half of its length is in water. The fundamental frequency of the air column is now

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Solution:

For the cylindrical tube open at both ends, $f=v / 2 l$.
When half of the tube is in water, it behaves as a closed pipe of length $l/ 2$.
$\therefore f^{\prime}=\frac{v}{4(l / 2)}=\frac{v}{2 l} $
$ \therefore f^{\prime}=f \text {. }$