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

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)  1:3  (B)  2:1  (C)  2:3  (D)  4:3

Tardigrade Admin · Accepted Answer

Frequency of fundamental note in closed pipe is

n^{'} = \frac{v}{4 l} ... (1)

Frequency of fundamental note in open pipe is

n^{''} = \frac{v}{2 l _{2}} ... (2)

Given,

n^{'} = n^{''}

∴ \frac{v}{4 l _{2}} = \frac{v}{2 l _{2}}

\Rightarrow l_{1} : l_{2} = 1 : 2

Note: A closed pipe produces only odd harmonics while an open pipe produces both the even and odd harmonics.

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

$1 : 3$

$2 : 1$

$2 : 3$

$4 : 3$