The frequency dependence of the hyperpolarizability (\ensuremath{\gamma}) of the nonrelativistic hydrogen atom is calculated for a range of third-order nonlinear optical processes using an expansion in Sturmian functions. It is shown that the quantitative relations between the various nonlinear optical processes are made much clearer when \ensuremath{\gamma} is treated as a function of an effective frequency ${\ensuremath{\omega}}_{L}$. The detailed, systematic exploration of the dispersion of \ensuremath{\gamma} of the hydrogen atom presented here should serve as a guide in the analysis and interpretation of experimental or theoretical results for less accessible systems.