Hi Ross, > .. > But aside from "rattling couplings" I'm wondering whether resonating > objects exhibit energy migration between modes? if so, why/how? > ..
Unless you want to go pretty deep in the higher maths (or an interest of mine: theoretical phyics), it isn't hard to come up with examples of this idea in a normally complex realm, as long as confusion about what the "energy" is is prevented. I mean talking about the "energy" of a sample is difficult 9square of the amplitude or so) but the energy of a reactive system is ok within high school physics, when for instance pondering on a mass spring system. The mass can be extended from the zero point, which puts a certain energy in the mass-spring combination, which during it's natural oscillation (normally harmonic, i.e. sinusoidal) will alternate between the potential energy and the kinetic energy. I've based a whole string simulation on these basic motion equations here: http://www.theover.org/Articles/string.html .
An easy example to visualize is a car driving over a bump: a single mass with 4 springs then exchanges energy between various modes.
De difficult thing when designing either physical or electronics examples of coupled resonating filters is to figure out the maximum amplitude, and the statistics of the resulting waves. At some point when combining input-output responses of coupled filters with resonances, connected probabilities come into play, which is an interesting but hard subject.
When looking at the acoustic vibration modes you mention, I would be careful with the "enrgy in a certain mode" assertion, because that can be defined in various ways, with different meanings. Also, the Helholz resonance modes of an space filled with air isn't quite the same as piece of metal exhibiting standing waves with certain amplitudes, so more exact definitions of the problem would be needed to work on that.
But, the coupled modes exist: put the damper of a piano and pluck and quickly damp a string; other strings will happily resonate along in all kinds of harmonic modes!
Theo V. -- dupswapdrop -- the music-dsp mailing list and website: subscription info, FAQ, source code archive, list archive, book reviews, dsp links http://music.columbia.edu/cmc/music-dsp http://music.columbia.edu/mailman/listinfo/music-dsp
