This is a nice little trick using Illustrator’s Blend option.
To create perfect sine-waves – or something very close – first of all, draw a line. Then go Filter > Distort > Zig Zag… and choose the number and height of waves you want (remembering to click the smooth radio button, otherwise you’ll get a zig zag).
Once this is done go Object > Expand Appearance to turn the wavy line into a proper vector.
You then need to copy this beautiful wavy line and create a distorted version on top of it. To do this simply copy (Cmd/Ctrl-C) the wavy line and paste in front (Cmd/Ctrl-F). Put one line on a locked layer and, with your Direct Selection Tool (A), drag the peaks and troughs of the curves either up or down randomly. See below where the blue triangle is.
Then unlock the original wave and go Object > Blend > Blend Options… and select the number of Specified Steps you want. Then, with both selected, go Object > Blend > Make (Cmd/Ctrl-Option-B).