You know, there is a tone generator in AE. Cool. You could feed it some sine waves and then move the plot point of an emitter around. Just saying.

Here's the code on the tone generator- a sine wave multiplied by another sine wave that's been wrapped in an absolute method, that's then added to the keys, which are then looped.

Math.sin(time*5)*50) * Math.abs(Math.sin(time*4)) + effect("Tone")("Frequency 1").loopOut("cycle")

Feel free to move Frequency2-5 around or change the tone waveform options around, and chart the result.

Check out the file here-

movecraft.com/clients/movecraft/tone_generator.zip