First slide

Stationary waves

Question

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 air column is now

Moderate

A

$f$
B

$f / 2$
C

$3 f / 4$
D

$2 f$

Solution

$I n c a s e 1, L e n g t h o f a i r c o l u m n = l a n d f u n d a m e n t a l f r e q u e n c y = f ∴ f = \frac{v}{2 l} I n c a s e 2, L e n g t h o f a i r c o l u m n = \frac{l}{2} a n d f u n d a m e n t a l f r e q u e n c y = f' ∴ f' = \frac{v}{4 \frac{l}{2}} = \frac{v}{2 l} \Rightarrow f' = f$

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