Here's a link that someone might enjoy. It shows some properties of non-linear acoustics.
http://www2.erasmusmc.nl/Thoraxcente.../superharm.htm
This is basically where the intensity of a wave source is high enough that the medium doesn't propagate the signal without generating "distortion", though the distortion generated is typically of a growing harmonic structure, I'm rather certain there are ways to even have the signal become chaotic (for example, within a resonant chamber).
Another interesting possible correlation with this phenomenon could be similar to the decay of high energy particles in collisions - space would then ideally be a perfectly linear medium and not distort the information (though at very high energies, vacuum energies might not even be linear ... virtual particles anyone?).
Another idea that's interesting to combine with this is the possibility of a unique time reference for an observer and the possibility of aliasing http://www.dataq.com/applicat/articles/sample-rate.html.
As a quick example, imagine traveling space through a set of rings and taking pictures as you passed through them. If you take a picture every 1 second but it takes you 10 seconds to move from one to the next, then you have a sequence of 10 images than shows this repetition.
Let's say instead that you moved 10 times as fast. Well in this case the pictures would show the rings being stationary, so 10 times as fast appears as stopping altogether. Going 9 times as fast would make the rings appear to have reversed direction.
If we combine these two ideas together and assume there could exist some fundamental observer reference for time (which is implied by both relativity and quantum mechanics), then if we have some waveform becoming distorted into higher and higher harmonics. It could potentially reach a point at which the frequency appeared to drop and this could appear to be in a quick chaotic fashion as well.
In a similar sense, let's say we kept going 3 times as fast between each picture and we could describe the results as being in 1 of 10 possible states.
t=1, we have a velocity of 1 and position of 1
(We'll assume the velocity immediately becomes 3 times as fast after the picture is taken to avoid Calculus and additional fractal components)
t=2, we were at position 1 but have a velocity of 3 and reach position 4
t=3, we move from 4, at a velocity of 3^2=9 and arrive at position 4+9=13, which appears as 13 mod 10=3
t=4, we continue doing this and take a picture at (13+3^3=40 or position 0)
t=5 is position 40+3^4=121, or position 1
t=6 is position 4
t=7 is position 3
...
So we have the observations of these rings moving semi chaotically (much like uncertainty in quantum physics) as the sequence 1,4,3,0,1,4,3 though actually the pattern does repeat. ...0143014301430...
So it has a wavelength, but an additional component that can be very difficult to predict. Notice also that in a non-linear medium, this can be a dynamic rate of change as the density of the distortion/wave is altered over time.
Anyway, those were just a couple thoughts I figured someone might enjoy.


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