Analytical solutions to the one-dimensional advection-dispersion equation are presented for several cases where the source concentration is either input continuously at a periodically fluctuating level or input as a single pulse of finite duration. The solute of interest can undergo linear equilibrium adsorption. Both semi-infinite and infinite flow domains are considered. The solutions are utilized to quantify the degree to which the traveling contaminant pulses are attenuated (damped) as they migrate through an aquifer. The degree of damping is shown to be related to two dimensionless parameters and this relationship is conveniently presented in graphical form. The analytical results compare favorably with the behavior of trace organic contaminant pulses observed during injection of advanced-treated wastewater into a shallow, alluvial aquifer in the Palo Alto Baylands.