A numerical solution for the propagation of the Alfv¿n waves produced by Io is presented. The waves are shown to interact strongly with the torus and magnetic field inhomogeneities. We find substantial reflection occurs from the magnetospheric medium and only about a quarter of the wave power will reach the ionosphere on its first pass. It is concluded that both WKB and ray tracing arguments are inappropriate, contrary to previous studies. A more realistic picture may be that of a whole field line or L shell resonating in an eigenmode. We discuss the Alfv¿n structure behind Io and comment upon some possible features that it may exhibit. In particular it may be possible to produce decametric arcs that are more closely spaced than ray tracing permits by exciting higher harmonic eigenmodes of Io's L shell. ¿American Geophysical Union 1987