Question

A closed organ pipe and an open organ pipe are tuned to the same fundamental frequency. What is the ratio of their lengths?

• A. $1:2$
• B. $2:1$
• C. $2:3$
• D. $4:3$

Answer 1

Answer: (A)

$1:2$

Answer 2

Avoiding end correction, the length of closed organ pipe, is $l_{1}=\frac{\lambda_{1}}{4} \text { or } \lambda_{1}=4 l$ The length of open organ pipe, is $l_{2}=\frac{\lambda_{2}}{2}$ or $\lambda_{2}=2 l_{2}$ Here, $n_{1}=n_{2}$ $\Rightarrow \frac{v}{\lambda_{1}}=\frac{v}{\lambda_{2}}$ or $\frac{v}{4 l_{1}}=\frac{v}{2 l_{2}}$ Therefore, $l_{1}: l_{2}=1: 2$