First slide

Standing waves

Question

The fundamental frequency of a closed pipe is 220Hz. If $\frac{1}{4}$ of the pipe is filled with water, the frequency of the first overtone of the pipe now is

Moderate

A

220 Hz
B

440 Hz
C

880 Hz
D

1760 Hz

Solution

Fundamental frequency of closed pipe
$n = \frac{v}{4 l} = 220 Hz \Rightarrow v = 220 \times 4 l$
If $\frac{1}{4}$ of the pipe is filled with water then remaining length of air column is $\frac{3 l}{4}$
Now fundamental frequency = $\frac{v}{4 (\frac{3 l}{4})} = \frac{v}{3 l} and$
First overtone = 3 x fundamental frequency

= $\frac{3 v}{3 l} = \frac{v}{l} = \frac{220 \times 4 l}{l} = 880 Hz$

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