We have developed a simple computer code that simulates the electromagnetic response of a simplified magnetosphere with respect to pressure variations at the magnetopause. The dependence of the magnetospheric response on the azimuthal wave number of the magnetopause perturbation and possible effects of a kinetic correction to the Alfvén wave dispersion are investigated. We find that the coupling of the cavity mode to Alfvén oscillations is most efficient for wave numbers m = 1 … 3. With increasing wave number, the fundamental cavity mode may lower its eigenfrequency, opposed to the behavior of the higher‐order modes. Kinetic effects cause a propagation of Alfvén wave energy away from the resonant field line.