We have examined the propagation of sudden impulses (SI) by an MHD numerical simulation in the three-dimensional magnetosphere to assess the precision of the Tamao travel time approximation and the dynamic properties of preliminary impulses (PI). The results show that the propagation of SI signals is strongly influenced by the inhomogeneous Alfv¿n velocity profile, and the region of high Alfv¿n velocity immediately outside the plasmasphere allows the signals to reach ionospheric altitudes in the shortest time possible. At the ionospheric altitude, the simulated arrival time of the PI, defined by the first peak in wave amplitude, is in extremely good agreement with Tamao's prediction throughout the range of invariant latitudes connected to the outer magnetosphere. The arrival time at invariant latitudes within the plasmasphere, however, is slightly earlier than Tamao's prediction because of the fact that the impulse deviates from a point source as it arrives at the plasmapause. In contrast, the onset time of the PI, which corresponds to the first deflection in the magnetic field, varies little with invariant latitude, consistent with the well-established observations of the nearly simultaneous PI onset without the need to invoke the Earth-ionosphere waveguide model. Our simulation also shows that the differentiation in PI arrival time strongly influences the evolution of the ionospheric convection vortices. The twin vortices first appear slightly above the latitude connected to the plasmapause, and they move poleward because of the late arrival of impulse signals at higher latitudes. Another pair of vortices appears later at plasmaspheric latitudes owing to the delay of signals by the dense plasmasphere. Our results not only provide quantitative assessment on the Tamao path, which can benefit future development in travel time magnetoseismology, but they also demonstrate the evolution of PI-induced ionospheric convection vortices by incorporating the propagation characteristics of MHD waves.