A linear, one-dimensional gyrofluid code has been used to determine the characteristics of propagating Alfv¿n waves and the ionospheric Alfv¿n resonator on a Jupiter-Io flux tube. This model includes electron inertia, electron pressure gradient, and finite ion gyroradius effects, as well as the displacement current correction to prevent the Alfv¿n velocity from exceeding the speed of light. A quasi-steady Vlasov code provides realistic density profiles along the flux tube as input parameters for the gyrofluid model. In this paper, we demonstrate that the majority of the wave energy from an initial pulse with a long wavelength (~0.1 RJ) is unable to reach Jupiter's ionosphere without wave breaking, phase mixing, and/or other nonlinear processes; however, a significant energy flux may be transferred via high-frequency, small-wavelength waves to the ionosphere. The waves that reach the ionosphere stimulate an ionospheric Alfv¿n resonator which is generated between the ionospheric boundary and the first velocity peak of the Alfv¿n phase speed. The ionospheric density and scale height play important roles to determine the resonant frequency. The eigenfrequency decreases with increasing scale height and with increasing ionospheric density. The fundamental frequency and higher harmonics of the Alfv¿n resonator are comparable to the observed reoccurring frequency of S bursts between a few and hundreds of Hz. On the basis of this information, we suggest the Alfv¿n resonator as the likely driver explaining multiple occurrences of S bursts.