Definition:Periodic Wave/Wave Number

Definition

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

$\forall x, t \in \R: \map \phi {x, t} = \map f {x - c t}$

The wave number $k$ of $\phi$ is the number of complete wavelengths of $\phi$ per unit distance along the $x$-axis.

Also known as

The term wave number can also be seen as wavenumber.

Also see

• Wave Number of Periodic Wave: this wave number is shown to be $\dfrac 1 \lambda$, where $\lambda$ is the wavelength of $\phi$

• Results about wave number can be found here.

Sources

• 1955: C.A. Coulson: Waves (7th ed.) ... (previous) ... (next): Chapter $\text {I}$: The Equation of Wave Motion: $\S 3$