First of all, it depends on the size and shape of the plate. As a rule of thumb, the wave length cannot be longer than two times the extent of the object, which gives us the rough estmate of frequency as
A more precise answer requires finding the eigenmodes of the plate (i.e., solving the sound wave equation with the boundary conditions imposed by the shape of the object).
If we assume that the plate is very big, then we have to account for other processes that may affect the wave existence/propagation. E.g., in the case of a very long wavelength (very small frequency) the random displacements of atoms in respect to each other may be more significant than those corresponding to the wave. There are also many damping mechanisms that play more important role at low frequencies, and can make a wave non-propagating.