The properties of the coupling of compressional and transverse ULF waves strongly depend on the azimuthal wavenumber m. We investigate these effects in a numerical model of ULF wave propagation in a dipolar magnetosphere. As the azimuthal wave number m becomes larger, the frequencies of the global modes are increased, each coupling location is shifted toward the plasmapause, and the wave energy of global compressional modes in the magnetosphere is confined to a smaller region near the magnetopause. These conclusions are qualitatively consistent with previous analytical and numerical models. It is suggested that the radial dependence of the azimuthal wavelength in the dipole geometry is important to the propagation of compressional waves. This effect is not present in either box or cylindrical models, in which the azimuthal wavelength does not depend on the radial distance, and can be distinguished from effects arising from the inhomogeneity of the Alfven speed. On the other hand, the Alfven shear modes are found to have periods independent of m.