Equation of Harmonic Wave/Wavelength and Velocity

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:
 * $\map \phi {x, t} = a \map \cos {\dfrac {2 \pi} \lambda \paren {x - c t} }$

where $\lambda$ is the wavelength of $\phi$