## [Audacity-nyquist] Raliegh Waves Model

 [Audacity-nyquist] Raliegh Waves Model From: paul beach - 2010-12-08 01:42:37 ```The generall topic is vibrations of an elastic solid. The solution to surface vibrations, or Raliegh waves, is given as, u = A (e^-rz - e^-sz) sin k(x - ct) w = A (e^-rz - e^-sz) cos k(x - ct), from "The Earth", Harold Jeffreys, 1923. He says that no other type of harmonic wave is capable of continuous propagation over the surface of a homogeneous solid. The subtraction of one exponential from another is of interest. This would represent, to me, different dampings in (two) different directions. Since this is a feature of every musical instrument; the rather subtle amplitude modulations should sound convincing. One instrument has a large surface area, and roars like an earthquake--the church organ. Try the method of exponential differences with some music, Ellen Bayne by Stephen Forster, http://www.climatehoax.ca/music/ellen_bayne.mp3 74k 37 sec. Audacity Progam, How and Why The ear does not respond to stationary phase differences, that is, x = sin, y = cos sounds the same as, x = sin, y = sin. On the other hand octave couplings are common on the Organ, so the difference of exponentials times frequency is summed. (exp^a - exp^b) * sin f ; fundamental (exp^c - exp^d) * sin 2f ; second octave (exp^e - exp^e) * sin 4f ; third octave ;nyquist plug-in ;version 1 ;type generate ;name "Exponential Differences_Organ..." ;action "Generating E.D. ..." ;control p "Pitch" int "Frequency" 69 22 122 (stretch 2 (lp (scale 3.0 (sim (mult ( sim (mult 1.0 (exp-dec 0 0.08 1)) (mult (- 0.0 1.0) 1.0 (exp-dec 0 0.04 1)) ) (sine p ); first octave ) (mult 1.0 ( sim (mult 1.0 (exp-dec 0 0.02 1.0)) (mult (- 0.0 1.0) 1.0 (exp-dec 0 0.010 1.0)) ) (sine (+ 12 p ) ) ; second octave ) (mult 1.0 ( sim (mult 1.0 (exp-dec 0 0.01 1.0)) (mult (- 0.0 1.0) 1.0 (exp-dec 0 0.005 1.0)) ) (sine (+ 24 p ) ) ; third octave ) ) ; end sim ) ; end scale 180) ; end low pass filter ) ; end stretch -- paul beach sniffyraven@... ```

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