The velocity for wave propagation is derived by writing down a
differential equation which describes the wave propagation phenomenon. For linear media and non-dispersive
media the wave equation takes the form
Any function of the form 
is a solution to this differential
equation. We can easily convince ourselves of this
by taking the second time derivative:
Inserting in Eq. 13 we see that the differential equation
is satisfied irrespective of the specific functional form of f(x).