Strange thought.
If I have a round tank of water and a plunger in the center and I run the plunger as such that I create a standing wave.
If the sides of the tank can move, make the diameter larger or smaller,, then as this standing wave pushes on the sides they move out lowering the water level so the plunger moves down to accommodate.
The frequency of the plunger would also need to change but the effect of a standing wave stays constant.
As the tank grows in diameter the waves would change and I think the standing wave would get shorter and then the pressure on the sides of the tank would get smaller but the surface area they are pushing on gets larger due to the increase in diameter.
In essence then the tank has stored the change in frequency,, if it is a resonant system and you are creating a standing wave the input energy stays the same but the frequency changes and the resonant growth is zero so the cost does not increase either,, meaning if there were no other losses the input cost would only be the increase in frequency and the resonant relationship would give back the energy costs to drive the system so the input then would be the same as if you just expanded the diameter,, so it is like you push the water down and expand 2 steps and the water gives back one step and then your next push is 2 steps,,
I know it is stupid,, but you have just made a resonant system that has a changing frequency,,, and as the frequency goes up the input cost per cycle goes down,, less push distance per stroke, less return distance,, blah blah blah,,
