Flutern wrote: ↑Thu Aug 25, 2022 11:15 amI say this without malice, but what you write about sound waves (and acoustics) doesn't make any sense to me. If you're really into that sort of stuff, you might find it useful to get a better understanding of complex waveforms, standing waves and the acoustics of open tubes, instead of speculating about where this or that wave might "inhabit" in the bore of the flute. Here's a nice introduction to the acoustics of flutesGreenWood wrote: ↑Thu Aug 25, 2022 7:54 am I understand well enough how the sound wave forms in a flute, and around first open tonehole is the effective end of flute in 2nd octave also, where full venting is allowed below that.
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You yourself say the wave is cut in half, so my reason tells me that you agree there are two waves. One inhabits the region towards the embouchure and the other towards the lower end.
Oh, I think I take criticism for whatever it is worth. For example ad hominem is supposed a failure to argue rationally, or condescension might be seen as prejudiced conceit or even a form of assumed entitlement. Etc.
I don't expect my view to be understood, and frankly I'm really not into the mathematical representation of waveforms and similar, but take a more "mechanical" approach. I will explain the difference. Mathematical models are drawn from measurements of the resulting waveform from any particular arrangement. From those a picture is deduced of how the whole has interacted at any one point in time, and the parameters that effect that whole are calculated into a reliable equation. That is fine by me, it works, and I understand the picture it represents.
My view though is based on trying to understand the detail of how a waveform is achieved based on a progressive sequence of realtime events. That is to say, I am looking at how one particular pressure wave acts as it reflects at the end of the bore, interacts with similar on its return journey, and around TH1 has the effect of interfering with an incoming wave to the extent of shifting its pitch higher, so setting up a new standing wave pattern that suits bore length, not TH1 frequency. There is no other way I can think of for D2 (TH1 lifted) to sound but by interaction from a reflected wave at bore end, a flute will just play C# at TH1 otherwise.
Either way, the wave of D2 in lower part of flute will be different from higher part, they will not be mirror of each other because pressure differences at ends are different, bore characteristics are different along each part, TH1 is situated differently to ideal node position for each half. The result will be that the wave shape (sound not length) in lower bore, will be different and influence that of the top half by interference with it - in other words it creates a new sound based on the reflection of the wave formed in the lower bore. At this point we are talking soundform, not wavelength, because the wavelength has already become harmonized to D2.
I'm ok to agree to disagree, and do not mean to complicate how others approach all of this.