Question

An open organ pipe has fundamental frequency of $300\text{Hz}$. The first overtone of this organ pipe is same as the first overtone of a closed organ pipe. Find the length of the closed organ pipe?
[speed of sound in air $=330\text{m/s}$]

• A. $45\text{cm}$
• B. $41\text{cm}$
• C. $42\text{cm}$
• D. $48\text{cm}$

Answer 1

The correct option is B $41\text{cm}$

Fundamental frequency of open organ pipe,
$f_o=300\text{Hz}$
So, its first overtone$(n=2)$,
$f_1=2f_o=2\times 300=600\text{Hz}$
Now, first overtone of closed organ pipe $(n=3)$,
$f_1^{{}^{\prime }}=\frac{3v}{4l}$
$\Rightarrow 600=\frac{3\times 330}{4l}$
$\Rightarrow l=0.41\text{m}=41\text{cm}$