Sensor designed to determine the mass flow of a liquid, said sensor comprising: at least a measuring tube (A, B) designed to conduct the liquid, wherein the measuring tube (A, B) has an end section on the inlet side and an end section on the outlet side; at least a carrier body on which the measuring tube is fixed in the area of the end section on the inlet side and in the area of the end section on the outlet side; at least an exciter designed to excite vibrations of the at least one measuring tube (A, B) in at least one vibration mode; at least two vibration sensors (14, 16) designed to measure vibrations of the measuring tube and to output signals that depend on the vibrations; an operation and evaluation circuit designed to drive the at least one exciter, to receive the vibration-dependent signals of the vibration sensors (14, 16) and to determine a sequence of measured values representing a mass flow as a function of at least a sequence of time-discrete measuring signals, each presenting a phase difference between the vibration-dependent signals of the vibration sensors, wherein the operation and evaluation circuit comprises an adaptive low-pass filter designed to filter the sequence of the measured values representing the mass flow; wherein the low-pass filter has at least a filter parameter that depends on at least an adaptive control variable, characterized in that the adaptive control variable depends, in turn, on the gas load of the medium being measured, and in that the operation and evaluation circuit is designed to determine the control variable as a function of a fluctuation of a natural frequency of the measuring tube vibration, said fluctuation being dependent on the gas load. at least a measuring tube (A, B) designed to conduct the liquid, wherein the measuring tube (A, B) has an end section on the inlet side and an end section on the outlet side; at least a carrier body on which the measuring tube is fixed in the area of the end section on the inlet side and in the area of the end section on the outlet side; at least an exciter designed to excite vibrations of the at least one measuring tube (A, B) in at least one vibration mode; at least two vibration sensors (14, 16) designed to measure vibrations of the measuring tube and to output signals that depend on the vibrations; an operation and evaluation circuit designed to drive the at least one exciter, to receive the vibration-dependent signals of the vibration sensors (14, 16) and to determine a sequence of measured values representing a mass flow as a function of at least a sequence of time-discrete measuring signals, each presenting a phase difference between the vibration-dependent signals of the vibration sensors, wherein the operation and evaluation circuit comprises an adaptive low-pass filter designed to filter the sequence of the measured values representing the mass flow; wherein the low-pass filter has at least a filter parameter that depends on at least an adaptive control variable, characterized in that the adaptive control variable depends, in turn, on the gas load of the medium being measured, and in that the operation and evaluation circuit is designed to determine the control variable as a function of a fluctuation of a natural frequency of the measuring tube vibration, said fluctuation being dependent on the gas load.