Hello Chad,
I started to answer your question and was doing a little research on the web. (My expertise in wave motion of fluids is limited to childhood experiments in a bath tub and, later on in life, flies in my martini glass) I typed "speed of waves in a tray of water" into Google and came with an answer on our own web site! Go to the site and type 2223 into the search box. There are several items there that address your question.
The basic point is that the differential equations for surface waves in shallow water are quite different from those in deep water or those of electromagnetic waves in vacuum or those of sound in gasses and solids. The solutions no longer follow the v=λf rule.
If you want to play around a bit, try varying the depth of water in the pan and plotting the speed as a function of the depth.
LeeH
(published on 02/09/2012)
