Question

An open organ pipe has a fundamental frequency of $300Hz$. The first overtone of a closed organ pipe has the same frequency as the first overtone of open organ pipe. How long is each pipe?

• A. $41.25cm$
• B. $42.3cm$
• C. $49.5cm$
• D. $40.5cm$

Answer 1

The correct option is A $41.25cm$

Fundamental frequency of an organ pipe
$f_1=\frac{v}{2l_0}$
$\therefore l_0=\frac{v}{2f_1}=\frac{330}{2\times 300}=0.55m$
Given, first overtone of closed pipe $=$ First overtone of open pipe
Hence, $3\left(\frac{v}{4l_c}\right)=2\left(\frac{v}{2l_0}\right)$
$\Rightarrow l_c=\frac{3}{4}{l}_0=\left(\frac{3}{4}\right)\left(0.55\right)$
$\Rightarrow l_c=0.4125m\Rightarrow l_c=41.25cm$