Question

A closed organ pipe of length $10\text{cm}$ has fundamental frequency equal to half the value of the second overtone of an open organ pipe. The length of the open organ pipe will be

• A. $10\text{cm}$
• B. $20\text{cm}$
• C. $30\text{cm}$
• D. $40\text{cm}$

Answer 1

The correct option is C $30\text{cm}$

Length of closed organ pipe, $l=10\text{cm}=0.1\text{m}$
So, fundamental frequency,
$f_1=\frac{v}{4l}=\frac{v}{4\times 0.1}=\frac{5v}{2}$
Length of open organ pipe, $l=?$
So, for second overtone $(n=3)$,
$f_2=\frac{nv}{2l}=\frac{3v}{2l}$
Given, $f_1=\frac{f_2}{2}$
Hence,
$\frac{5v}{2}=\frac{3v}{4l}$
$\Rightarrow l=0.3\text{m}=30\text{cm}$