Following Henyey and Pomphrey (1983), we investigate the spectrum of small-scale internal waves using the eikonal method. We send test-wave packets through background internal-wave shear fields, varying the initial distributions and the background spectra. We find that the test-wave distributions evolve to Garrett-Munk wave number spectra for all the cases investigated. We find that the test waves evolve toward higher frequencies, in contrast to a simple induced diffusion model, and consistent with a picture of low-frequency internal-wave sources.