The velocity potential can be expressed as:
Does 
satisfy the Laplace equation? Why?
The constants A and B can be determined from satisfying the Kinematic b.c. on the bottom of the sea and the linearized dynamic b.c. on the free-surface 
It can be shown that finally:
Finally, by applying the kinematic b.c. on the free-surface we get:
Eqn. (64) is called the dispersion relationship (Finite Depth Water)
Useful Definitions/Formulas:
