This Demonstration generates Lissajous curves, with the look and feel of an oscilloscope as used in electrical engineering. You can choose from various waveforms and control the amplitude, phase, and frequency for both and components. You can also hear how the respective functions sound by clicking the speaker buttons. Trace the curves using the slider "fraction of cycle". Animate the phase to get the feel of independent time bases that are not locked in.
Mathematically, Lissajous curves are a subset of parametric curves where and are sine functions. Since, in this Demonstration, other waveforms can be chosen, one could call the parametric curves "generalized Lissajous curves".
Thanks to the author's students from the winter 2008 Mathematica course who implemented this concept.
More can be found at the author's website.