An apparatus for ascertaining and/or monitoring a process variable, especially density of a medium. The apparatus includes: an exciting/receiving unit, which excites a mechanically oscillatable unit to execute mechanical oscillations and which receives the mechanical oscillations; an electronics unit, which applies to the exciting/receiving unit an electrical, exciter signal, and which obtains from the exciting/receiving unit an electrical, received signal. The electronics unit produces the exciter signal in such a manner, that, between the received signal and the exciter signal, a phase difference equal to a desired value of phase difference results, at which effects of changes of viscosity on mechanical oscillations of the mechanically oscillatable unit are negligible, and that the desired value of phase difference is predetermined as a function of the ratio of impedance of the exciting/receiving unit to the input impedance of the electronics unit.