The invention relates to a device for determining and/or monitoring at least one physical or chemical process variable, for example, the level, viscosity or density of a medium in a container, comprising at least one mechanically oscillatory unit (1) and at least one drive/receiving unit (8). The mechanically oscillatory unit consists of a tube (2) and of an inner oscillator (3). The tube (2) is connected via an end (4) oriented away from the process to a fastening unit (5), and the end (6) of the tube (2) oriented toward the process is provided as a free end. The fastening unit is connected directly or, optionally, via another element to the container inside of which the medium is located. The tube (2) surrounds the inner oscillator (3), and the inner oscillator (3) is fastened to an end (7), which is oriented toward the process and which is located at the end (6) of the tube (2) also oriented toward the process. The drive/receiving unit (8) sets the mechanically oscillatory unit (1) in oscillatory motion or it receives the oscillations of the mechanically oscillatory unit (1). The invention provides that the inner oscillator (3) has at least one groove/narrowing (9) that determines at least the oscillation frequency of the mechanically oscillatory unit (1).