A new experimental device for the determination of the dilatational dynamic surface elasticity of surfactant solutions has been developed. For the first time, the components of the surface elasticity of sodium dodecyl sulfate solutions are determined by longitudinal surface waves in the frequency range 0.8 - 5 Hz; this is the range where using other methods presents difficulties. It is shown that transverse (gravitational and capillary-gravitational) surface waves of the same frequency generated simultaneously in the measuring cell affect the measurement accuracy of the parameters of longitudinal surface waves. Plausible reasons for the differences between the results obtained experimentally and predicted by the diffusion theory of surfactant adsorption are discussed.