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The paper presents results of the laboratory acoustic measurements in the moist unloaded sand. For large saturations, only high-frequency fast longitudinal wave (type I wave according to Biot terminology) was observed. Its velocity is almost independent of humidity, and amplitude during gradual drying of the sand after running up to a certain maximum rapidly diminishes down to the complete disappearance of this wave. Low-frequency slow wave appears during further drying of the sample. Its velocity, amplitude and dominant frequency with humidity decreasing first grow to some maximum values, and then this wave attenuates too. To explain the observed effects for the slow wave, the mechanism based on the action of capillary cohesion is proposed.