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Physics — The Wave Equation

The 1-D wave equation, d'Alembert solution and 3-D form.

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\frac{\partial^2 u}{\partial t^2} = c^2 \frac{\partial^2 u}{\partial x^2}

u(x,t) = f(x - ct) + g(x + ct)

\nabla^2 u = \frac{1}{c^2}\frac{\partial^2 u}{\partial t^2}

k = \frac{\omega}{c}