A fluid measuring device for determining at least one characteristic property of a fluid includes a measuring tube having a fluid duct and a measuring section in which the measuring tube is cylindrical on the inside and an area of a measuring tube wall is configured as a waveguide, and a transmitter for exciting acoustic waves in the waveguide and a receiver for receiving acoustic waves which are in direct contact with an outer surface of the waveguide, wherein acoustic waves excited by the transmitter are adapted to propagate as a volume wave through the fluid. The waveguide has an elongated waveguide path which extends at an acute angle to a longitudinal extension direction of the measuring tube and with a component in the circumferential direction, wherein in the area of the waveguide path, the measuring tube wall has a smaller wall thickness than in areas adjoining the waveguide path.