Making wavey line with varying frequency and height

Hi, I'm trying to create a wavey line which decreases with frequency, as well as increasing in height as it goes along. So far all I have managed to do is create it manually (left part of the image below). The closest I can get to this within illustrator using automated processes is with the 'zig zag' distort and transform effect, which does not have an option for height.

My question is: is there a way of creating a line like the one on the left without having to do it manually? If not, does anyone have some tips as to how to do it manually - I can get it to look reasonably good, but it's fiddly and takes more time than I think it probably could)?

Thank you