We investigate optically excited terahertz standing spin waves in noncollinear magnetic bilayers. Using femtosecond laser-pulse excitation, a spin current is generated in the first ferromagnetic (FM) layer, and flows through a conductive spacer layer to be injected into the second (transverse) FM layer, where it exerts a spin-transfer torque on the magnetization and excites higher-order standing spin waves. We show that the noncollinear magnetic bilayer is a convenient tool that allows easy excitation of terahertz spin waves, and can be used to investigate the dispersion and thereby the spin-wave stiffness parameter in the thin-film regime. This is experimentally demonstrated using wedge-shaped Co and CoB (absorption) layers. Furthermore, t...