Question

The fundamental frequency of a closed organ pipe is equal to the first overtone frequency of an open organ pipe. If the length of open organ pipe is $80\text{cm}$ then the length of the closed organ pipe will be

• A. $30\text{cm}$
• B. $35\text{cm}$
• C. $40\text{cm}$
• D. $20\text{cm}$

Answer 1

The correct option is D $20\text{cm}$

Length of open organ pipe, $l=80\text{cm}=0.8\text{m}$
So, first overtone $(n=2)$,
$f_1=\frac{nv}{2l}=\frac{2v}{2\times 0.8}=\frac{5v}{4}$
Length of closed organ pipe, $l=?$
So, fundamental frequency $(n=1)$,
$f_2=\frac{nv}{4l}=\frac{v}{4l}$
Given, $f_1=f_2$
Hence,
$\frac{5v}{4}=\frac{v}{4l}$
$\Rightarrow l=0.2\text{m}=20\text{cm}$