It's Friday and I'm a nice guy and I felt like taking a crack at this.
Download this and apply to a shape layer: http://paulslemmer.pancakeapps.com/Motion_Goodies/AE_Presets/Shapes/SineWave.ffx
Noting that the frequency and speed of the wave doesn't change, I'd start with this. Take the audio keyframes, smooth them with something like smooth(8,5) and link the Wave Amp controller to it.
The hardest part with this method is going to be pinching those sides down, which you'll probably have to do with a distort effect.
Make a couple of them with different starting amplitude multipliers and strokes weights, and voila! Maybe. Ha.
That would be typical stuff for Trapcode Form. It would be super-simple there using an audio reactor. Still, you might be able to do it using the Audio Wave effect as well, but you would have to do quite some audio processing to get the delay and smoothing right... Other than that you can always use all sorts of other effects and tie them in with expressions of course...
You could use multiple copies of Audio Spectrum or Audio Waveform with different settings for height and different colors and thickness.
It would take some processing of the audio to smooth out the frequencies to get smooth curves.
Another option would be to use convert audio to keyframes to control the colors in a gradient used as a displacement map. None of the solutions I can think of except Trapcode Form can be achieved with a single copy of an effect.