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- vp is the phase velocity (in meter per second, m/s),
- ω is the angular frequency (in radians per second, rad/s),
- k is the wavenumber (in radians per meter, rad/m).
The phase speed gives you the speed at which a point of constant phase of the wave will travel for a discrete frequency. The angular frequency ω can not be chosen independently from the wavenumber k, but both are related through the dispersion relationship:
In the special case Ω(k)=ck, with c a constant, the waves are called non-dispersive, since all frequencies travel at the same phase speed c. For instance electromagnetic waves in vacuum are non-dispersive. In case of other forms of the dispersion relation, we have dispersive waves. The dispersion relationship depends on the medium through which the wave propagate and on the type of waves (for instance electromagnetic, sound or water waves). For sound waves, the more dense a medium is, the faster the waves will travel as particles will be closer together and thus energy can be transferred among them at a greater rate.
In almost all cases, a wave is mainly a movement of energy through a medium. Most often, the group velocity is the velocity at which the energy moves through this medium.
- A Treatise on The Mathematical Theory of Elasticity, A. E. H. LOVE, Dover Publications, New York.
- Dilbag Singh and S. K. Tomar, "Wave propagation in micropolar mixture of porous media" International Journal of Engineering Science, Volume 44, Issues 18-19 , November 2006, Pages 1304-1323.
- Weisstein, Eric W., "Wave velocity".