First slide

Stationary waves

Question

A cylindrical tube, open at both ends, has a fundamental frequency f₀ in air. The tube is dipped vertically into water such that half of its length is inside water. The fundamental frequency of the air column now is

Easy

A

$3 f_{0} / 4$
B

f₀
C

$f_{0} / 2$
D

2f₀

Solution

$n_{open} = \frac{v}{2 l_{open}}$
$n_{closed} = \frac{v}{4 l_{closed}} = \frac{v}{4 l_{open} / 2} = \frac{v}{2 l_{open}}$
$(As l_{closed} = \frac{l_{open}}{2})$ , i.e. frequency remains unchanged.

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