Apparatus designed to determine and/or monitor at least one process variable of a medium in a vessel with at least - a unit which is capable of vibrating, which comprises at least a membrane and at least a vibration element, - a drive/reception unit, which is designed to cause the unit, which is capable of vibrating mechanically, to vibrate in the vibration mode which corresponds to the vibration frequency by means of an electrical vibration signal of adjustable frequency, and to receive the mechanical vibrations from the unit which is capable of vibrating and to convert them to an electrical reception signal, wherein the vibration mode is a basic vibration mode and the excitation frequency is the basic resonance frequency corresponding to the basic vibration mode, and - an electronic unit, which is designed to generate the excitation signal from the reception signal and to determine the at least one process variable from the reception signal, wherein the membrane is connected to the drive/reception unit, wherein the vibration element has the shape of a vibration rod on which a paddle is formed at one end, and wherein said vibration element is secured to the membrane in the end area facing away from the paddle, characterized in that the mass distribution, the rigidity and the geometry of the unit which is capable of vibrating are selected in such a way that the frequency of at least a vibration mode (B') of the unit which is capable of vibrating that is higher in relation to the basic vibration mode is in the range between two neighboring whole-number multiples of the basic resonance frequency. - a unit which is capable of vibrating, which comprises at least a membrane and at least a vibration element, - a drive/reception unit, which is designed to cause the unit, which is capable of vibrating mechanically, to vibrate in the vibration mode which corresponds to the vibration frequency by means of an electrical vibration signal of adjustable frequency, and to receive the mechanical vibrations from the unit which is capable of vibrating and to convert them to an electrical reception signal, wherein the vibration mode is a basic vibration mode and the excitation frequency is the basic resonance frequency corresponding to the basic vibration mode, and - an electronic unit, which is designed to generate the excitation signal from the reception signal and to determine the at least one process variable from the reception signal, wherein the membrane is connected to the drive/reception unit, wherein the vibration element has the shape of a vibration rod on which a paddle is formed at one end, and wherein said vibration element is secured to the membrane in the end area facing away from the paddle, characterized in that the mass distribution, the rigidity and the geometry of the unit which is capable of vibrating are selected in such a way that the frequency of at least a vibration mode (B') of the unit which is capable of vibrating that is higher in relation to the basic vibration mode is in the range between two neighboring whole-number multiples of the basic resonance frequency. wherein the membrane is connected to the drive/reception unit, wherein the vibration element has the shape of a vibration rod on which a paddle is formed at one end, and wherein said vibration element is secured to the membrane in the end area facing away from the paddle, characterized in that the mass distribution, the rigidity and the geometry of the unit which is capable of vibrating are selected in such a way that the frequency of at least a vibration mode (B') of the unit which is capable of vibrating that is higher in relation to the basic vibration mode is in the range between two neighboring whole-number multiples of the basic resonance frequency.