The propagation of an impulse through a finite chain of monodisperse elastic beads was studied. The grain diameters progressively shrink in radius by a factor 'q' in a finite chain of elastic beads. The spatial symmetry of the solitary wave was destroyed due to the progressively shrink in radius. It was observed that the trailing part of the wave travelled progressively slower as comparative to the leading edge. It was shown that the shock waves can be thermalized by the construction of tapered chains.