In general, can we distinguish if a certain "wave" or disturbance $f$ which satisfies the wave equation \begin{equation} \frac{1}{v^{2}}\frac{\partial^2f}{\partial t^{2}}=\frac{\partial^2f}{\partial x^{2}}+\frac{\partial^2f}{\partial y^{2}} +\frac{\partial^2f}{\partial z^{2}} \end{equation} transverse or longitudinal? This is not necessarily electromagnetic - I am posing this as a general wave equation.

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?

In general, can we distinguish if a certain "wave" or disturbance $f$ which satisfies the wave equation \begin{equation} \frac{1}{v^{2}}\frac{d^2f}{dt^{2}}=\frac{d^2f}{dx^{2}} \end{equation} transverse or longitudinal? This is not necessarily electromagnetic - I am posing this as a general wave equation.

In general, can we distinguish if a certain "wave" or disturbance $f$ which satisfies the wave equation \begin{equation} \frac{1}{v^{2}}\frac{\partial^2f}{\partial t^{2}}=\frac{\partial^2f}{\partial x^{2}}+\frac{\partial^2f}{\partial y^{2}} +\frac{\partial^2f}{\partial z^{2}} \end{equation} transverse or longitudinal? This is not necessarily electromagnetic - I am posing this as a general wave equation.