An analogue for powers relation to displacement and frequency would be nice. Perhaps a dimensional analysis?
I’m not sure I can write a simple analogue, but here is a link with a derivation of power transported by a wave for the specific example for a traveling wave on a string: http://hyperphysics.phy-astr.gsu.edu/hbase/waves/powstr.html. (Click on “Show” for full derivation). In this case, the power is averaged over time.
