Equation of Harmonic Wave/Wave Number and Frequency

Theorem
Let $\phi$ be a harmonic wave which is propagated along the $x$-axis in the positive direction with constant velocity $c$.

Then the displacement of $\phi$ at point $x$ and time $t$ can be expressed using the equation:
 * $\map \phi {x, t} = a \map \cos {2 \pi \paren {k x - \nu t} }$

where:
 * $k$ is the wave number of $\phi$
 * $\nu$ is the frequency of $\phi$.