This question is a follow-up to this one, which fortunately I was able to successfully solve with the help of @Chris and @MarkusvonBroady:
How to create a seamless diagonal wavy pattern with opposing waves?
Now, on my shader nodes learning path, I'm trying to apply a gently noise to the pattern that smoothly follows the wavy curve.
I managed to get a noise into the pattern that is about what I imagine:
Only I am not clear with which parameters I should control this "distortion". My goal would be to add noise that slightly conforms to the curve, as seen in this bumbling sketch: