Another way to animate wavy lines is to apply the stroke effect to an animated mask shape.
Choose Layer>New>Solid or press Cmd+Y (Ctrl+Y).
Choose the Pen Tool from the Tools Palette and be sure the RotoBezier option is not selected. Draw a wavy mask with at least 3 vertex points in the Composition Window.
Make sure the layer is selected and choose Effect>Render>Stoke.
Choose Mask 1 as the path .
Keyframe the shape of your mask and change it over time.
You can also animate the start or end values of the Stroke Effect.
Lots of smoothly animated, different colored strokes make for great backgrounds.