Term information
The wave equation is an important second-order linear partial differential equation for the description of waves as they occur in physics such as sound waves, light waves and water waves. The wave equation is the prototypical example of a hyperbolic partial differential equation. In its simplest form, the wave equation refers to a scalar function u=(x1, x2,...,xn,t) that satisfies: { \partial^2 u \over \partial t^2 } = c^2 \nabla^2 u where \scriptstyle\nabla^2 is the (spatial) Laplacian and where c is a fixed constant equal to the propagation speed of the wave. This is known as the non-dispersive wave equation. source: http://en.wikipedia.org/wiki/Wave_equation
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"> <mrow> <mfrac> <mrow> <msup> <mo>∂</mo> <mn>2</mn> </msup> <mo>⁢</mo> <mi>u</mi> </mrow> <mrow> <mo>∂</mo> <mo>⁢</mo> <msup> <mi>t</mi> <mn>2</mn> </msup> </mrow> </mfrac> <mo>=</mo> <mrow> <msup> <mi>c</mi> <mn>2</mn> </msup> <mo>⁢</mo> <msup> <mo>∇</mo> <mn>2</mn> </msup> <mo>⁢</mo> <mi>u</mi> </mrow> </mrow> </math>
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"> <semantics> <mrow> <mfrac> <mrow> <msup> <mo>∂</mo> <mn>2</mn> </msup> <mi>u</mi> </mrow> <mrow> <mo>∂</mo> <msup> <mi>t</mi> <mn>2</mn> </msup> </mrow> </mfrac> <mo>=</mo> <msup> <mi>c</mi> <mn>2</mn> </msup> <msup> <mo>∇</mo> <mn>2</mn> </msup> <mi>u</mi> </mrow> <annotation encoding="SnuggleTeX">\[ { \partial^2 u \over \partial t^2 } = c^2 \nabla^2 u \]</annotation> </semantics> </math>