First slide

Standing waves

Question

A cylindrical tube, open at both ends, has a fundamental frequency ‘f’ in air. The tube is dipped vertically in water so that half of it is in water. The fundamental frequency of the air column is now :

Moderate

A

$\frac{f}{2}$
B

$\frac{3 f}{4}$
C

f
D

2f

Solution

Initially the tube was open at both ends and then it is closed. Further
$f_{o} = \frac{v}{2 l_{o}} and f_{c} = \frac{v}{4 l_{o}}$
Since, tube is half dipped in water, $l_{2} = \frac{l_{2}}{2}$
${∴ f}_{c} i = \frac{v}{4 (\frac{l_{o}}{2})} = \frac{v}{2 l_{o}} = f_{o} = f$
$∴$ correct option is (C).

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