Question

An open pipe, when closed at one end, can resonate in its third harmonic with a frequency which is $100Hz$ more than its fundamental frequency as an open pipe. If the fundamental frequency of the pipe when it is open at both ends is $50nHz$ , then the value of $n$ is

Answer 1

Answer: 4

Length of the organ pipe is same in both the cases. Fundamental frequency of open pipe is $f_1=\frac{v}{2l}$ Frequency of third harmonic of closed pipe will be.
$f_2=3\frac{v}{4l}$
Given that, $f_2=f_1+100$
$\text{ or }{f}_2-f_1=100$
$\text{ or }\frac{3}{4}\frac{v}{l}-\frac{1}{2}\frac{v}{l}=100$
$\Rightarrow \frac{v}{4l}=100$
$\therefore \frac{v}{2l}\text{ or }{f}_1=200Hz=50nHz$
$\Rightarrow n=4$
Therefore, fundamental frequency of the open pipe is $200Hz$. and $n=4$