Wave propagation through plasma crystals provides an interesting experimental approach towards understanding strongly coupled plasmas as well as certain solid state properties of crystals. In order to build up our basic understanding of conditions and processes, oscillation modes of one- and two-particle systems are investigated first, and the damping process is identified by studying the amplitude variations of the oscillations as a function of the excitation frequency. Next, single layer plasma crystals are investigated using the same techniques. An induced spontaneous transition from the solid to the gas phase is observed, and its possible origin is discussed.