Question

If a closed organ pipe of length $L_1$ in its fundamental mode resonates with an open organ pipe of length $L_2$, then $L_1:L_2$ is

• A. $1:2$
• B. $2:1$
• C. $1:4$
• D. $4:1$
• E. $1:8$

Answer 1

The correct option is A $1:2$

For open organ pipe
$n=\frac{v}{4l}=\frac{v}{4L_1}$
For closed organ pipe
$n=\frac{v}{2l}=\frac{v}{2L_2}$
$\frac{v}{4L_1}=\frac{v}{2L_2}$
$\frac{L_1}{L_2}=\frac{1}{2}$