The angular, or circular, wave number $k$, often misleadingly abbreviated as wave number, is the modulus of the wave vector. It is inversely proportional to the wave length $\lambda$.
The wave number is the spatial analogue of the angular frequency:
application of a Fourier transformation on data in the time domain
yields a frequency spectrum,
applied on data in the spatial domain (data as a function of position)
yields a spectrum as a function of the wave number.
Note that the exact definition of the wave number depends on the
physics field studied.
In mechanics, the angular wavenumber is defined as:
| $k=\displaystyle{\frac{2\pi}{\lambda}=\frac{2\pi f}{v_{\phi}}=\frac{\omega}{v_{\phi}}}$ | (1) |
where $f$ is the frequency (in Hertz), $\omega$ is the angular frequency (in rad.s-1) and $v_{\phi}$ is the phase velocity of the wave (in m.s-1).
Complex wave number
a commonly way to to account for losses
Complex and frequency dependent wave number
ac porous materials
.
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