The function

is a standing wave solution analogous to eq. (31.10)

for a surface gravity in an ocean of depth h. Following the derivation in the text, construct the kinetic and potential energy per unit area and find the dispersion relation for arbitrary h. Show that your solution has the correct limit for deep and shallow water. Answer:

where tanh x = sinh x / cosh x.  Show that the power density in this wave is the same as in a deep-water wave, eq. (31.20)