In the model of Complete and Incomplete Coordinate Systems, the velocity of the wave is represented by the value w. This variable can take on any value to represent the velocity of wave and medium under consideration. For example, when considering light waves traveling through a vacuum, we replace w with the value 299,792,458 meters per second, or by convention c. When considering light through air, its velocity decreases with increased density. In this case, we would first compute the new velocity and replace w with that value.
The equations apply to other wave types and mediums. For example, if we know the speed of sound through water (again taking density into account), then one would replace w with that value and again be able to use these equations. Similar, we could use the speed of sound through air. Thus, this model is generalized for all types of waves.
One of the exciting elements of this model, is that it places no limit of the maximum value that w can have and predicts other wave types and mediums with propagation characteristics far greater than the speed of light. If we discover a quantum wave medium, for example, these equations would still apply. In this case, we would simply replace w with that new value for the velocity of a quantum wave.
Remember, when an Incomplete Coordinate System meets or exceeds the speed of the wave, w, oscillations will not occur. But this does not mean that the coordinate system can’t go faster than w.
