The invention relates to a desity measuring device which is used to measure a density, rho, of a flowable medium and comprises measuring device electronics (ME) and a measuring transducer (MW) electrically connected to the measuring device electronics. The measuring transducer comprises a measuring tube (10), a vibration exciter (41) for exciting and maintaining vibrations, and a vibration sensor (51) for sensing vibrations of the at least one measuring tube. The measuring device electronics are designed to adjust, by means of a vibration measurement signal (s1) and an exciter signal (e1), a driving force that causes useful vibrations, namely vibrations having a specified useful frequency, fN, of the measuring tube, in such a way that a phase shaft angle, phi N, by which a velocity response, VN, of the measuring tube is phase shafted with respect to a useful force component, FN, of the driving force is less than -20 and greater than -80 degrees during a specified phase control interval, and / or the useful frequency has a frequency value that is more than 1.00001 times but less than 1.001 times a frequency value of an instantaneous resonance frequency of the measuring tube. Furthermore, the measuring device electronics are designed both to determine at least one frequency measured value, xf, representing the useful frequency for said phase control interval on the basis of the vibration measurement signal (s1) present during the phase control interval and to generate a density measured value, x rho, representing the density, rho, by using the frequency measured value, xf.