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Common woodwind instruments, as you know, are blown into from one of the two ends; the acoustic studies for air columns mainly center around these. But I am attempting to understand the acoustics of a woodwind instrument in which one does not blow into one of the ends but rather into a hole in the center, like the Chinese Koudi instrument.

In order to begin attempting to understand the acoustics of such an instrument, I need to know the fundamental frequency of the instrument. So let us say we only have the two open ends, and the hole you blow into (e.g. no tone holes). My first question is: What frequency would resonate based on the length of the instrument (also disregarding end correction for now)?

With that question answered (hopefully), let's say we covered one of the endholes with the blow hole and the other end hole still open, and still lacking tone holes. What frequency would resonate then, and how would it compare to the frequency from the first question?

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    You don't blow into one end of a western transverse flute either, but the two "halves" of the pipe are of different lengths, and one is closed at the end. The acoustics of the flute have been extensively researched - newt.phys.unsw.edu.au/music/flute is a good place to start. You may want to contact them directly about the Koudi - if anybody has published anything on its acoustics, they will probably know about it.
    – user19146
    May 25, 2016 at 19:55
  • @alephzero Oh I've been on that website you've linked there many times, which is where I gained most of my minimal acoustic knowledge, so it won't help me further (especially how they in fact treat the flute as being blown into from one end). I would love to contact them, but I wonder how quickly they would reply back, because I don't want to wait three months for an answer, though that's just me being selfish.
    – Sam
    May 26, 2016 at 23:08

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So let us say we only have the two open ends, and the hole you blow into (e.g. no tone holes). My first question is: What frequency would resonate based on the length of the instrument (also disregarding end correction for now)?

I believe this would behave as a regular tube open at both ends, but unable to resonate the fundamental, or in fact any odd harmonic, due to the open hole in the center. The embouchure hole would be acting like a permanent octave key. So I think the true fundamental wavelength would be twice the length of the instrument, but since you only have even harmonics it would be functionally the same as having the fundamental be simply the length of the instrument.

With that question answered (hopefully), let's say we covered one of the endholes with the blow hole and the other end hole still open, and still lacking tone holes. What frequency would resonate then, and how would it compare to the frequency from the first question?

If my thinking above is correct, then I think this would behave as a regular tube closed at one end, with fundamental wavelength 4x the length of the instrument. The embouchure hole being in the center doesn't disrupt the fundamental in this case. So compared to the first instrument, I think it would sound 2 octaves lower.

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  • How about someone buys a hunk of 1/4" ID tubing and builds a few of these to see what happens?
    – Carl Witthoft
    Oct 23, 2016 at 15:33

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