Quantifying the constitutive nonlinearity parameterβin fluids is of keyinterest for understanding ultrasonic propagation and its wide implications in medicaland industrial applications. However, current methods for ultrasonically measuring itshow large limitations in that the signal is only valid at a reduced and unjustifiedspatial range away from the transducer. This is not consistent with the fact thatβshould be constant everywhere in the fluid and independently of the ultrasonicexperimental setup. To overcome this, the nonlinear wave propagation equations arerigorously derived and the ensuing differential equation is numerically solved. As asecond contribution, the experimental and model information sources are treated underthe information theory context to probabilistically reconstructβ, providing not onlyits value, but also the degree of confidence on it given both sources of data. This methodis satisfactorily validated testing the repeatability ofβin water varying distances,energies, frequencies, and transducer setups, yielding values compatible withβ= 3.5.
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