The most general form of the wave equation may be given as $\frac{\partial^2f(x,t)}{\partial t^2}+v^2\frac{\partial^2f(x,t)}{\partial x^2}=0$ in one dimension, where naturally for a multi-variable function in n dimensions, we rewrite in terms of the [[Laplace operator]] ($\nabla^2$) applied to $f(\mathbf{x},t).$ Thus where we also use a more elegant notation for the time derivative we rewrite the equation as $\partial^2_tf(\mathbf{x},t)+v^2\nabla^2 f(\mathbf{x},t) = 0.$ $v$ is the [[wave velocity]]. # Discussion ## context The wave equation is related to the [[transport equation]]. ## meaning of $v.$ # Solution #Mechanics/WaveMechanics #MathematicalFoundations/Analysis/DifferentialEquations