Question

The frequency of the fundamental note of a closed organ pipe and that of a open organ pipe are same.What is the ratio of their lengths?

Answer 1

If you start with the same fundamental frequency for both open and closed, say f0f0, you'll notice that for the Open pipe, the harmonics are:

f0,2f0,3f0,...

f0,2f0,3f0,...

While for the closed,

f0,3f0,5f0,...

f0,3f0,5f0,...

And you'll notice that the closed pipe has greater spacing of harmonics compared to the open pipe.

That is for a given single note. You have to lower the note of the closed pipe by 12f012f0 (1 octave) to produce the same spacing of harmonics as the open pipe.