Experiments to determine the frequency autocorrelation function of an electronic transition (the "solvation function") inherently depend on a multidimensional response function. However, a degenerate transient absorption experiment, or "single-wave length transient hole burning" (SW-THB), provides a one-dimensional cut through this multidimensional space with sufficient information to uniquely determine the desired solvation function. We derive an analytical formula that relates the solvation function to the one-dimensional SW-THB signal. Sample calculations examine the effects of strong versus weak coupling to the solvent, the wavelength of the laser relative to the absorption spectrum and of unresolved fast relaxation components. We conclude that for many systems, SW-THB provides a simpler alternative to multidimensional methods for measuring solvation dynamics.