Distinguishing transverse and longitudinal from 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?