Wave Number of Harmonic Wave/Proof 1
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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 wave number $k$ of $\phi$ can be expressed as:
- $k = \dfrac 1 \lambda$
where $\lambda$ is the wavelength of $\phi$.
Proof
By definition, a harmonic wave is an instance of a periodic wave.
Hence Wave Number of Periodic Wave can be used directly.
$\blacksquare$