Question

An open pipe is suddenly closed at one end with the result that the frequency of third harmonic of the closed pipe is found to be higher by 100 Hz than the fundamental frequency of the open pipe. The fundamental frequency of the open pipe in Hz is

Answer 1

Fundamental frequency of open organ pipe
$=\frac{v}{2l}=n$
Third harmonic of closed pipe
$=\frac{3v}{4l}=n^{\prime }$
Now $n^{\prime }-n=100\text{Hz}$
Put the values of v and v' here-
$\frac{3v}{4l}-\frac{v}{2l}=100$

$\frac{3v-2v}{4l}=100=\frac{v}{4l}$
So, $\frac{v}{2L}=2\times 100$

$\Rightarrow \frac{v}{2L}=n=200\text{Hz}$