Question

The third harmonic of a closed organ pipe is equal to the second overtone of an open organ pipe. If the length of open organ pipe is $60\text{cm}$, then the length of closed organ pipe will be

• A. $20\text{cm}$
• B. $30\text{cm}$
• C. $40\text{cm}$
• D. $50\text{cm}$

Answer 1

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

Length of open organ pipe, $l=60\text{cm}=0.6\text{m}$
So, second overtone $(n=3)$,
$f_1=\frac{nv}{2l}=\frac{3v}{2\times 0.6}=\frac{5v}{2}$
Length of closed organ pipe, $l=?$
So, third harmonic $(n=3)$,
$f_2=\frac{nv}{4l}=\frac{3v}{4l}$
Given, $f_1=f_2$
Hence,
$\frac{5v}{2}=\frac{3v}{4l}$
$\Rightarrow l=0.3\text{m}=30\text{cm}$