High-resolution electron energy loss spectroscopy was used to study the electronic properties of (3/2 × 3/2)-Na/Cu(1 1 1) at room temperature. Loss spectra showed two-well distinct losses at 114 and 180 meV assigned to not dispersive charge density waves. Mechanisms to explain their existence are proposed. Moreover, the expected 2D plasmon of the Na quantum well state was not observed. The strong influence of the underlying Cu substrate may be responsible for the absence of such mode.