Spin wave resonances are calculated for two exchange coupled ferromagnetic films with different magnetic anisotropies. In this structure a domain wall can be pinned near the interface and affect spin wave frequencies. We find that the exchange spring can decrease the decay length of excitations at the interface by enhancing the frequency mismatch between the two films. We also propose the function of such a structure as a spin wave "valve." Dipolar contributions to the spin wave energies are estimated using a method adapted from an effective medium approximation in the magnetostatic limit.