Density waves are structures in planetary rings generated by periodic perturbing forces. Classic models of these structures assume that both the period and amplitude of these perturbations are strictly constant. Extending these models to situations where the period of the perturbing force varies over time reveals that the observed structure of these waves can be translated into a relatively straightforward record of the recent history of the periodic perturbations acting on the rings. For example, the structure of density waves in Saturn’s rings generated by satellites with time-variable orbits can be transformed into records of the moons’ orbital periods over the past several years (e.g., Tiscareno et al. 2006, ApJL). Moreover, there are multiple density waves that appear to be generated by time-variable asymmetries in Saturn’s gravitational field. Analysis of these waves yields maps of how both the amplitudes and periods of these gravitational anomalies changed over the course of several decades, providing a new window into the planet’s interior.