In General Relativity, the wave equation is typically introduced as mere a toy model for gravitational perturbations. While it is true that solutions to Einstein?s Equations are fundamentally more complex, understanding the propagation of waves within such solutions provides insight about some of their geometric features. In this talk, I will look at the case of asymptotically anti-de Sitter black holes and discuss how their conformal boundary at infinity (and boundary conditions imposed there) influences the dispersion of waves.