Question

The fundamental frequency of an open organ pipe is $300Hz$. The first overtone of this pipe has same frequency as the first overtone of a closed organ pipe. If speed is $328m/s$, then the length of closed organ pipe is

• A. 41 cm
• B. 37 cm
• C. 31 cm
• D. 80 cm

Answer 1

The correct option is A 41 cm

First overtone of open organ pipe is, $f=\frac{2v}{2l}=\frac{v}{l_1}$
First overtone of closed organ pipe is, $f=\frac{3v}{4l_2}$
Given :

$\frac{v}{l_1}=\frac{3v}{4l_2}$ $\Rightarrow l_2=\frac{3l_1}{4}$

$l_1=\frac{\lambda }{2}\Rightarrow \frac{v}{2f}=\frac{328}{2\times 300}=\frac{41}{75}$

$l_2=\frac{3l_1}{4}=\frac{41}{100}=41cm$