Wave propagation

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Wave propagation is any of the ways in which waves travel through a medium (waveguide).

With respect to the direction of the oscillation relative to the propagation direction, we can distinguish between longitudinal wave and transverse waves.

Another useful parameter for describing the propagation is the wave velocity that mostly depends on some kind of density of the medium.

For electromagnetic waves, propagation may occur in a vacuum as well as in a material medium.

1 Wave velocity
2 See also
3 References
4 External links

[edit] Wave velocity

Seismic wave propagation in 2D modelled using FDTD method in the presence of a landmine

Wave velocity is a general concept, of various kinds of wave velocities, for an electromagnetic wave's phase and speed concerning energy (and information) propagation. The relationship between group velocity and phase velocity is the dispersion relationship:

$v_p = \frac{\omega}{k}$

The dispersion relation gives you the speed at which a point of constant phase of the wave will travel for a discreet frequency (hence phase velocity). The speed at which a resultant wave packet from a broad range of frequencies will travel is called the group velocity and is determined from the gradient of the dispersion relation:

$v_g = \frac{\delta \omega}{\delta k}$

In almost all cases, a wave is merely a movement of energy through a medium.

Wave velocity is the speed at which the energy moves through this medium. 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.

The wave dispersion equation is:

$v=f\lambda=\frac{\lambda}{T}=\frac{\omega}{k}$

where

v

is the wave velocity ([LT ⁻¹]; m/s);

λ

is the wavelength ([L]; m);

f

is the frequency ([T ⁻¹]; Hz or ¹⁄_s);

T

is the period ([T]; s);

ω

is the angular frequency (rad Hz or ^rad⁄_s); and,

k

is the wavenumber (^rad⁄_m).

[edit] See also

[edit] References

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".