Abstract
An integral equation relating the thermal noise’s pressure measured by an acoustothermometer to the one-dimensional temperature profile of a waterlike medium is derived by applying the fluctuation-dissipative theorem to hydrodynamic equations. On the basis of this equation, effects of the quasi-stationary field of thermal radiation, a strong absorption of acoustic waves in the medium, and a finite beam width of the receiving antenna are investigated. Conditions under which the solution to the equation coincides with the result of the transfer theory, which ignores the aforementioned effects, are determined. The role of the effects under study in acoustothermometry of biological media is investigated. A method is proposed for controlling the depth from which the radiation is received. This method allows the retrieval of the temperature profile of the medium from the data of acoustic sounding.
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