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 ..... $Hz$
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(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 with 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$.
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