Editing Equations of motion (section)

===Wave equations===

Equations of wave motion are called ''[[wave equation]]s''. The solutions to a wave equation give the time-evolution and spatial dependence of the [[amplitude]]. Boundary conditions determine if the solutions describe [[traveling wave]]s or [[standing waves]].

From classical equations of motion and field equations; mechanical, [[gravitational wave]], and [[electromagnetic wave]] equations can be derived. The general linear wave equation in 3D is:

<math display="block">\frac{1}{v^2}\frac{\partial^2 X}{\partial t^2} = \nabla^2 X  </math>

where {{math|''X'' {{=}} ''X''('''r''', ''t'')}} is any mechanical or electromagnetic field amplitude, say:<ref>{{cite book | title = University Physics | author1 = H.D. Young | author2=R.A. Freedman | year=2008 | edition=12th|publisher=Addison-Wesley (Pearson International) | isbn = 978-0-321-50130-1}}</ref>

* the [[Transverse wave|transverse]] or [[Longitudinal wave|longitudinal]] [[Displacement (vector)|displacement]] of a vibrating rod, wire, cable, membrane etc.,
* the fluctuating [[pressure]] of a medium, [[sound pressure]],
* the [[electric field]]s {{math|'''E'''}} or {{math|'''D'''}}, or the [[magnetic field]]s {{math|'''B'''}} or {{math|'''H'''}},
* the [[voltage]] {{math|''V''}} or [[Electric current|current]] {{math|''I''}} in an [[alternating current]] circuit,

and {{math|''v''}} is the [[phase velocity]]. Nonlinear equations model the dependence of phase velocity on amplitude, replacing {{math|''v''}} by {{math|''v''(''X'')}}. There are other linear and nonlinear wave equations for very specific applications, see for example the [[Korteweg–de Vries equation]].