Frequency of Harmonic Wave/Proof 1

Theorem

Let $\phi$ be a harmonic wave expressed as:

$\forall x, t \in \R: \map \phi {x, t} = a \map \cos {\omega \paren {x - c t} }$

The frequency $\nu$ of $\phi$ can be expressed as:

$\nu = \dfrac 1 \tau$

where $\tau$ is the period of $\phi$.

Proof

By definition, a harmonic wave is an instance of a periodic wave.

Hence Frequency of Periodic Wave can be used directly.

$\blacksquare$