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Thank you everyone for all the great input. 

Combining many of the tricks and tips you offered, and a special shoutout to Nicolle Fuller and Ikumi, this is what I did to make the variable sine wave.
Create a horizontal line longer than the sine curve needed. Using the ZigZag effect, tweak the line to match the predominant wavelength. From the Object menu click Expand appearance. 
Working  left of center, use the scissor tool (C) to cut the line where the curve starts to expand or narrow from the predominant wavelength. Then, holding down the shift key, use the Select tool (V) to squeeze or expand the curve (pulling to the left). Continue this process until the variable curves to the left of center match the variable curve.
Repeat the process right of center. 
When all the cuts and curve had been adjusted, use the Direct Select tool (A) to rejoin the open anchor points. Toggle the connect tangents to clean up/smoothe the connecting joints.
Try it. It’s fast and works really well!!

Marj

Leggitt Design
303.394.0566
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