Velocity of Periodic Wave is Wavelength times Frequency

Theorem
Let $\phi$ be a periodic wave expressed as:
 * $\forall x, t \in \R: \map \phi {x, t} = \map f {x - c t}$

where $c$ is the velocity of $\phi$.

Then:
 * $c = \nu \lambda$

where:
 * $\nu$ is the frequency of $\phi$
 * $\lambda$ is the wavelength of $\phi$.