The elastodynamic behavior of polycrystalline cubic materials is studied through the fundamental propagation properties, the attenuation and wave speed, of a longitudinal wave. Predictions made by different analytical models are compared to both numerical and experimental results. The numerical model is based on a three-dimensional Finite Element (FE) simulation which provides a full-physics solution to the scattering problem. The three main analytical models include the Far-Field Approximation (FFA), the Self-Consistent Approximation (SCA) to the reference medium, and the herein derived Second Order Approximation (SOA). The classic Stanke and Kino model is also included, which by comparison to the SOA, reveals the importance of the distribution of length-scales described in terms of the two-point correlation function in determining scattering behavior. Further comparison with the FE model demonstrates that the FFA provides a simple but satisfactory approximation, whereas the SOA shows all-around excellent agreement. The experimental wave velocity data evaluated against the SOA and SC reveal a better agreement when the Voigt reference is used in second order models. The use of full-physics numerical simulations has enabled the study of wave behavior in these random media which will be important to inform the ongoing development of analytical models and the understanding of observations.