The nature of one-dimensional voidage waves in a liquid-fluidized bed that has been subjected to external perturbations and is exhibiting instabilities has been investigated both experimentally and numerically. Voidage waves that consist of alternating regions of high and low solid concentrations were observed to form and travel in a coherent manner along the fluidized bed. Solid particles were observed to move upward when a dense phase of the wave passed through their positions; otherwise, the particles settled downward. The voidage waves formed as a result of instability in such liquid-fluidized-bed systems are traveling waves with dense and dilute phases being convected along the bed. However, the motion of individual particles was observed to be highly restricted to a small region in space over short time scales. A diffusive type of behavior was observed where particles drifted gradually away from their initial positions within the bed. This type of motion was adequately described by a simple dispersion model used in the present study.