https://en.wikipedia.org/wiki/Wave_equation
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Introduction
The wave equation is a partial differential equation that may constrain some scalar function u = u (x1, x2, …, xn; t) of a time variable t and one or more spatial variables x1, x2, … xn. The quantity u may be, for example, the pressure in a liquid or gas, or the displacement, along some specific direction, of the particles of a vibrating solid away from their resting positions. The equation is
{\displaystyle {\frac {\partial ^{2}u}{\partial
t^{2}}}\;=\;c^{2}\left({\frac {\partial ^{2}u}{\partial
x_{1}^{2}}}+{\frac {\partial ^{2}u}{\partial x_{2}^{2}}}+\cdots +{\frac {\partial ^{2}u}{\partial x_{n}^{2}}}\right)}{\displaystyle {\frac {\partial ^{2}u}{\partial t^{2}}}\;=\;c^{2}\left({\frac {\partial ^{2}u}{\partial x_{1}^{2}}}+{\frac {\partial ^{2}u}{\partial x_{2}^{2}}}+\cdots +{\frac {\partial ^{2}u}{\partial
x_{n}^{2}}}\right)}
where c is a fixed non-negative real coefficient.
Using the notations of Newtonian mechanics and vector calculus, the wave equation can be written more compactly as
{\displaystyle {\ddot {u}}=c^{2}\nabla ^{2}u}{\displaystyle {\ddot {u}}=c^{2}\nabla ^{2}u}
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