Determination of Absolute Sound Levels and Acoustic Absorption Coefficients by Thermocouple Probes--Theory

A detailed theoretical analysis of the operation of thermocouple probes used to determine absolute sound levels or acoustic absorption coefficients is presented. The probe consists of a thermocouple imbedded in a sound absorbing medium which closely matches in density and sound velocity the medium in which the sound level is to be determined. In use the transducer which generates the acoustic field is excited to generate sound pulses with a rectangular envelope. The initial time rate of change of the temperature at the thermocouple junction is determined. In addition to the measurement of the temperature change, the calculation of the absolute sound intensity requires only a knowledge of the absorption coefficient of the imbedding material and its heat capacity per unit volume at the temperature at which the measurements are made. The theoretical discussion includes an analysis of the relation between the temperature rise at the junction resulting from absorption in the body of the imbedding medium and the sound level. In addition, the effects of (a) viscous forces arising from relative motion between the thermocouple and the imbedding fluid and (b) heat conduction between the thermocouple and the fluid, in contributing to the temperature change at the thermocouple junction are analyzed. Based on the analysis, a set of design formulas is obtained which are summarized and illustrated for the convenience of other investigators who may wish to design and use such probes.