Difference between revisions of "Dictionary:Wave equation"

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The foregoing are forms of the <b>scalar wave equation</b> These forms do not provide for the conversion of P-waves to S-waves nor vice-versa.  
 
The foregoing are forms of the <b>scalar wave equation</b> These forms do not provide for the conversion of P-waves to S-waves nor vice-versa.  
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The <b>vector wave equation</b> is more general; it is  
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The <b>vector wave equation</b> is more general; for isotropic media it is  
  
 
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If <math> \nabla \cdot \Psi =0 </math>, this gives an S-wave; if <math> \nabla \times \Psi =0 </math>, a P-wave. The wave equation in polar anisotropic (transversely isotropic) media is given in Figure [[Special:MyLanguage/Dictionary:Fig_T-13|T-13]].
 
If <math> \nabla \cdot \Psi =0 </math>, this gives an S-wave; if <math> \nabla \times \Psi =0 </math>, a P-wave. The wave equation in polar anisotropic (transversely isotropic) media is given in Figure [[Special:MyLanguage/Dictionary:Fig_T-13|T-13]].
 
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For a derivation, and the relation of the ''wave equation'' to the ''equation of motion'', see the main page: [[Wave equation]].

Latest revision as of 15:38, 27 September 2020

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An equation that relates the spatial and time dependence of a disturbance which can propagate as a wave. In rectangular coordinates x, y, z, it is

,

where represents wave displacement (pressure, rotation, dilatation, etc.) and V the velocity of the wave. Functions are solutions to this equation.

In spherical coordinates where r is the radius, the colatitude, and the longitude, the wave equation becomes:

The foregoing are forms of the scalar wave equation These forms do not provide for the conversion of P-waves to S-waves nor vice-versa.


The vector wave equation is more general; for isotropic media it is

,

which can be written in component form as

.


If , this gives an S-wave; if , a P-wave. The wave equation in polar anisotropic (transversely isotropic) media is given in Figure T-13.


For a derivation, and the relation of the wave equation to the equation of motion, see the main page: Wave equation.