Question

The fundamental frequency of an open organ pipe is 300 Hz.The first overtone of the pipe has same frequency as first overtone of a closed organ pipe. If speed of sound is 330 m/s, then the length of the 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

For open pipe, $n=\frac{v}{2l}$, where $n_0$ is the fundamental frequency of the open pipe.

$\therefore l=\frac{v}{2n}=\frac{330}{2\times 300}=\frac{11}{20}$

As frequency of first overtone of open pipe $=$ frequency of first overtone of closed pipe.
$\therefore 2\frac{v}{2l}=3\frac{v}{4l^{\prime }}\Rightarrow l^{\prime }=\frac{3l}{4}=\frac{3}{4}\times \frac{11}{20}=41.25cm$