The included steps are:
1 - Start with a standard, straight, 2-point path.
2 - Apply Effect > Distort > Zig Zag.
3 - Create a "Top Object" in the shape of a triangle, that is the desired shape of your taper. Again, a basic shape, 3-points, no curves.
4 - Make sure this top object is layered above the zig zag, then select both the zig zag and the top object and Object > Envelope Distort > Make with Top Object.
Then add an additional path to the tip as needed.
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