Frequency-dependent conductivities of the two-dimensional sodium-ion conductor Na-beta''-alumina, of composition Na1.70Li0.32Al10.66O17, have been taken between 100 MHz and several THz, at different temperatures. In their low-frequency sections, the spectra are affected by the polycrystallinity of the sample, i.e. by inter-grain polarization, while the vibrational component prevails in the far infrared. In a first step, these two contributions are identified and removed from the spectra. In a second step, the remaining frequency-dependent conductivities are explained in terms of the displacive movements performed by the sodium ions within the crystal volume. Here, two kinds of motion are distinguished. One is translational via vacant local residence regimes, establishing macroscopic transport. The other is localized within a residence regime. The experimental conductivities are well reproduced by model spectra. The values of the parameters used agree with the available structural information.