The invention relates to a method for the additive manufacturing of a three-dimensional workpiece from a liquid material (1), in which method the liquid material (1) is fed to a displacement chamber (2) and discharged in drop form via a jet hole (4) by means of a pressure pulse which is generated with the aid of a reciprocating piston (3) delimiting the displacement chamber (2). According to the invention, in order to optimise the wetting properties of at least one surface (5, 6) which delimits the displacement chamber (2) and/or the jet hole (4), sound waves are coupled into the liquid material (1) for a limited period of time with the aid of the piston (3) which is caused to vibrate for this purpose. The invention also relates to a device for carrying out the method according to the invention.