When two simple waves are combined, but one is rotated out of phase with respect to the other, the result is no longer a sine wave, but a combination of the frequencies, the rotational phase difference, and any time offset between the two original waves. Such a combination of sine waves, when graphed or otherwise visually displayed is known as a Lissajous figure.

In mathematics, sine waves are the result of graphing such as y=sin(x) for enough values of x to provide a smooth oscillating curve about the x axis. The function x=sin(y) is 90 degrees out of phase with y=sin(x) because it creates a curve which oscillates about the y axis. In the physical world, perhaps the best known example of sine waves is sound. The frequency of a sine wave is the distance, or time span, between each "crest...