Harmonics Theory, Part 5: Nonlinear Waves Make Harmonics

by Ray Tomes

Harmonics Theory: Nonlinear Waves make Harmonics

This blog series from FSC Science Director Ray Tomes will share the fundamentals of physics in layman's terms, showing how present theory must inevitably lead to all waves losing energy and forming harmonically related waves. The end result is a very specific detailed structure that matches the observed universe and explains many previously mysterious observations. This series was previously published.

Nonlinear Waves Make Harmonics

In any nonlinear system waves will develop harmonics. This means that wave shapes gradually change over time. An example of this is when ocean waves approach the shore the wave velocity changes with changing depth and so the peaks of waves begin to catch up to the troughs, eventually breaking.

Consider a standing wave that fills the entire universe or, if you think the universe is infinite, then consider a large wave that satisfies some characteristic conditions of the universe. If the wave equation for the universe were linear, then such a wave would carry on wobbling in place for ever, never interacting with itself. However as the wave equation is nonlinear the wave must change shape over time. For example, this changing in shape might be to have a sharper peak and flatter trough.

In presently accepted cosmology there may not be sufficient time in the universe for very large waves to develop in shape due to nonlinearities. However the indication is that the measured parameters of such models show an acceleration parameter, which is another way of saying that the past may have been much longer than the initial indications. For the purpose of what follows the assumption will be made that there is no difficulty with large universal waves existing for very many cycles, which means that very particular values of cosmological parameters are necessary.

When a wave has a shape different from a sine wave, it is said that harmonics are present. Real musical instruments also have this property as when we pluck a guitar string it makes waves that fit not just one wave in the string, but also other waves that fit two, three, four and more waves exactly into the string. These other waves will always divide the original wave by an integer, and in the linear situation will have frequencies which are exact multiples of the fundamental wave.

The three dimensional universe is no different in this respect, the fundamental wave will have harmonics which are exact divisions of the wavelength, and if the nonlinearity is not too great, multiples of the original frequency. However something additional happens in three dimensional standing waves that does not happen in the one dimensional case of the guitar. By the interaction of the three dimensions, these new waves also become standing waves and through the nonlinearity also produce harmonics. This production of further harmonics by the harmonics is something that has not previously been investigated. Be ready for some entirely new understanding of the nature of waves in the universe.