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

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

BHUBHU 2003

Solution:

Frequency of fundamental note in closed pipe is
$n'=\frac{v}{4 l} \,\,\,...(1)$
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Frequency of fundamental note in open pipe is
$n''=\frac{v}{2 l_{2}} \,\,\,\,...(2)$
Given, $ n'=n'' $
$\therefore \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.