The notion of magnetic field line resonance has been very effective in explaining many features of long-period geomagnetic pulsations. To date the decoupled transverse wave equations have been solved in a magnetic dipole field, whereas only WKB approximate solutions have been used in more general geometries. We have developed a solution of the decoupled equations that includes both a general magnetic field geometry and the effects of density and mass composition. The aim of this paper is to isolate and examine the effect on eigenfrequencies of only the field geometry by keeping density constant along all field lines. We review the diurnal variations in wave period predicted on the ground and in space by using the recent Olson--Pfitzer magnetospheric magnetic field model in our solution. For example, on the ground at 67¿ magnetic latitude the diurnal variation in period caused by field geometry is larger than a factor of 2. At 6.6 RE, where the dipole field line from 67¿ crosses the magnetospheric equator, there is negligible diurnal variation in period. Significant diurnal variations in period (>10%) at fixed radial distance in the equatorial plane in space occur only at distances >10RE. Knowledge of the field geometry is shown to be important for the determination in mass density in space from ground pulsation observations. We discuss the impact of our results in interpretation of experimental data.