In theory, stratified media in which the layers are elastically homogeneous and isotropic approximate transversely isotropic media with an axis of symmetry perpendicular to layering when the seismic wavelength is sufficiently longer than the layer spacing. The phenomenon has been attributed to fine scale bedding laminations. We have made a partial test by making laboratory measurements of compressional-wave velocities parallel and perpendicular to layering in fabricated samples consisting of glass and epoxy. We found no statistically significant difference between observation and theory in this limited test. Further, having used several frequencies, we found that the velocities progressively change from the long-wave values toward those predicted by the time-average relation, as expected. Finally, it has been proposed that the long-wave approximation holds when the ratio of the seismic wavelength to layer thickness (lambda /d) is 10-100. We found that the minimum ratio was highest in the midrange of composition (half glass, half epoxy), even though the samples in that range have the smallest combined layer thickness. This result suggest that the frequency dependence of anisotropy in layered media is a function of the proportions of the materials as well as the thickness of the layers.--Modified journal abstract.