First slide

Standing waves

Question

A cylindrical tube, open at both ends, has a fundamental frequency / 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

f/2
B

3f/4
C

f
D

2f

Solution

For open pipe $f = \frac{V}{2 l}$
for closed pipe $f^{â²} = \frac{V}{4 l^{â²}} = \frac{V}{4 (l / 2)} = \frac{V}{2 l}$
$f^{â²} = f$

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