There are more than wall vibrations... they have been still not invistigated. 🙂
Wall vibrations, then, are also transitory process...
I don't remember right now (I should re-read the relative article)... but since we are talking about a transitory you have to study the passing from note to note, from dynamic to dynamic... and the speed of the variations.
Of course in a stationary process is much more easier to study.
It's clear if you don't consider the attack of the note, of every note at every dynamic... you can barely can distinguish a wind instrument from a string instrument.
Or... if you are in the mid register... an alto saxophone from a tenor saxophone...
It's like when you record a long note, you go to the wave editor/DAW, you cut the very first milliseconds of the sample (the attack of the note)... and then you reproduce the sample.
What do you get? 🙂
For example... nobody have never considered the axial stiffness of the body... and... (try to imagine for a moment).