In this paper we use results from numerical computations to suggest relationships between a compactly supported potential and its scattering frequencies. The potential can be time independent or can vary periodically with time. In some cases there are rigorous proofs of our conjectures, while in other cases our conjectures remain open mathematical problems. We conjecture that the scattering frequencies of time-independent potential asymptoticaaly approximate the diameter of the support of the potential. We also demonstrate that there exist positive, time-periodic potentials with growing modes and that the scattering frequencies of highly oscillatory potentials converge to the scattering frequencies of a suitably averaged time-independent potential as the frequency of oscillation tends to infinity.