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wave equation

The PDE $u_{tt} = c^2u_{xx}$ (or its higher-dimensional analog) modeling a disturbance that propagates at a fixed speed $c$ .

The wave equation $u_{tt} = c^2\nabla^2u$ (one spatial dimension: $u_{tt}=c^2u_{xx}$ ) describes a disturbance -- a string's displacement, a pressure wave -- that propagates through a medium at fixed speed $c$ .

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