Wavenumber–frequency diagram

Origins

In general, the relationship between wavelength \lambda, frequency \nu, and the phase velocity v_{p} of a sinusoidal wave is:

:v_\text{p} = \lambda \nu

Using the wavenumber (k=2\pi/\lambda) and angular frequency (\omega=2\pi\nu) notation, the previous equation can be rewritten as

:v_\text{p} = \frac{\omega}{k}

On the other hand, the group velocity is equal to the slope of the wavenumber–frequency diagram:

:v_\text{g} = \frac{\partial\omega}{\partial k}

Analyzing such relationships in detail often yields information on the physical properties of the medium, such as density, composition, etc.

References

References

1. (1990). "An introduction to atmospheric physics". [[Academic Press]].
2. J. Pedlosky. (1998). "Geophysical fluid dynamics". [[Springer (publisher).