Can we distinguish if a general wave or disturbance $f$ (not necessarily electromagnetic) which satisfies the wave equation \begin{equation} \frac{1}{v^2}\frac{\partial^2 f}{\partial t^2} = \frac{\partial^2 f}{\partial x^2} + \frac{\partial^2 f}{\partial y^2} + \frac{\partial^2 f}{\partial z^2} \equiv \nabla^2 f \end{equation} is transverse or longitudinal?
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