Let us consider a function f1(x, t) defined by the relation
where a, b, and g are all positive. The function is periodic both in x and in t and varies between ±a. It can be shown to represent a wave of amplitude a, propagating in the direction of +x with velocity g/b. If x is increased by δx and t by δt then
where, vω is called the phase velocity. The function f1(x, ...