The radiation pressure of a chopped laser beam is used to excite low-frequency (f = 0.4-5 Hz) waves in plasma crystals. The first system studied is a linear chain of spherical plastic particles of m diameter. The second system is a single-layer crystal with hexagonal structure made of the same kind of particles. The measured dispersion and damping of longitudinal compressional waves is compared with a model for dust lattice waves in a system of particles interacting by Yukawa-type potentials. From the best fit the shielding factor is determined. The finding that the measured shielding length is comparable with the interparticle distance is supported by Monte Carlo simulations.