en>Kiril Simeonovski: How can the standard deviation of 90, 100, 110 be 8.16 when it obviously equals 10?

2014-01-20T00:03:15Z

How can the standard deviation of 90, 100, 110 be 8.16 when it obviously equals 10?

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'''Wave propagation''' is any of the ways in which [[wave (physics)|wave]]s travel.

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

For [[electromagnetic wave]]s, propagation may occur in a vacuum as well as in a material medium. Other wave types cannot propagate through a vacuum and need a [[transmission medium]] to exist.

== Wave velocity ==
{{see|phase velocity|group velocity|signal velocity}}
[[Image:Seismic wave prop mine.gif|thumb|400px|right|[[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 a wave's [[phase (waves)|phase]] and [[speed]] concerning energy (and information) propagation. The [[phase velocity]] is given as:

:<math>v_p = \frac{\omega}{k},</math>

where:
*''v<sub>p</sub>'' is the phase velocity (in meters per [[second]], m/s),
*''ω'' is the [[angular frequency]] (in [[radian]]s 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 (waves)|phase]] of the wave will travel for a discrete frequency. The angular frequency ''ω'' cannot be chosen independently from the wavenumber ''k'', but both are related through the [[dispersion relation]]ship:

:<math>\omega = \Omega(k).\,</math>

In the special case {{nowrap|''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 wave]]s 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 waves propagate and on the type of waves (for instance [[electromagnetic wave|electromagnetic]], [[sound wave|sound]] or [[ocean surface wave|water]] waves).

The speed at which a resultant wave packet from a narrow range of frequencies will travel is called the [[group velocity]] and is determined from the [[gradient]] of the [[dispersion relation]]:

:<math>v_g = \frac{\partial \omega}{\partial k}</math>

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.

== See also ==
* [[Absorption (electromagnetic radiation)]]
* [[Antenna theory]]
* [[Diffraction]]
* [[Huygens–Fresnel principle]]
* [[Photon]]
* [[Polarization (waves)]]
* [[Radio propagation]]
* [[Reflection (physics)]]
* [[Refraction]]
* [[Scattering]]
* [[Wave]]

== References ==
*{{cite book
|author=A.E.H. Love
|title=A Treatise on The Mathematical Theory of Elasticity
|publisher=[[Dover Publications|Dover]]
|location=New York
|year=
|isbn=
}}
*{{cite web
|author=E.W. Weisstein
|url=http://scienceworld.wolfram.com/physics/WaveVelocity.html
|title=Wave velocity
|work=[[ScienceWorld]]
|year=
|accessdate=2009-05-30
}}

== External links ==
*[http://www.kuleuven.be/bwm/edt A matlab toolbox for seismic wave propagation] at [[Katholieke Universiteit Leuven]]
*[http://math.ucr.edu/~jdp/Relativity/EM_Propagation.html Animation] How an electromagnetic wave propagates through a vacuum
*[http://www.acoustics.salford.ac.uk/feschools/waves/propagation.htm Propagation of sound waves]

[[Category:Wave mechanics]]

Relative standard deviation - Revision history

en>Kiril Simeonovski: How can the standard deviation of 90, 100, 110 be 8.16 when it obviously equals 10?