We present a simple time-of-flight analysis of Alfv¿n pulsations standing on closed terrestrial magnetic field lines. The technique employed in this study in order to calculate the characteristic period of such oscillations builds upon earlier time-of-flight estimates via the implementation of a more recent magnetospheric magnetic field model. In this case the model employed is the Tsyganenko (1996) field model, which includes realistic magnetospheric currents and the consequences of the partial penetration of the interplanetary magnetic field into the dayside magnetopause. By employing a simple description of magnetospheric plasma density, we are therefore able to estimate the period of standing Alfv¿n waves on geomagnetic field lines over a significantly wider range of latitudes and magnetic local times than in previous studies. Furthermore, we investigate the influence of changing season and upstream interplanetary conditions upon the period of such pulsations. Finally, the eigenfrequencies of magnetic field lines computed by the time-of-flight technique are compared with corresponding numerical solutions to the wave equation and experimentally observed pulsations on geomagnetic field lines.