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Q.
The fundamental frequency of a closed pipe is $220 \,Hz$. If $1/4$th of the pipe is filled with water, the frequency of the first overtone of the pipe now is
AFMCAFMC 2007
Solution:
Fundamental frequency of closed pipe
$ n=\frac{v}{vl}=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} $
First overtone $ =3\times $ fundamental frequency
$ =\frac{3v}{3l}=\frac{v}{l}=\frac{220\times 4l}{l} $
$ =880\,Hz $