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

A) $220\ Hz$
B) $440\ Hz$
C) $880\ Hz$
D) $1760\ Hz$
Explanation

(c) Fundamental frequency of closed pipe
$n = \frac{v}{4l} = 220\ Hz \Rightarrow v = 220 \times 4l$
If $\frac{1}{4}$ of the pipe is filled water then remaining length of air column is $\frac{3l}{4}$
Now fundamental frequency $= \frac{v}{4\left( \frac{3l}{4} \right)} = \frac{v}{3l}$ and
First overtone $= 3 \times$ fundamental frequency
$= \frac{3v}{3l} = \frac{v}{l} = \frac{220 \times 4l}{l} = 880\ Hz$

Dr. Abubacker
Reviewed by Dr. Abubacker

Physics Educator & NEET/JEE Specialist

Ph.D. in Physics with 19+ years of teaching experience.

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