The problem is to calculate the attenuation of plane sound wavespassing through a viscous, heat-conducting fluid containing small sphericalinhomogeneities. The attenuation is calculated by evaluating the rateof increase of entropy caused by two irreversible processes: (1) the mechanicalwork done by the viscous stresses in the presence of velocity gradients,and (2) the flow of heat down the thermal gradients. The method isfirst applied to a homogeneous fluid with no spheres and shown to give theclassical Stokes-Kirchhoff expressions. The method is then used to calculatethe additional viscous and thermal attenuation when small spheres arepresent. The viscous attenuation agrees with Epstein's result obtained in1941 for a non-heat-conducting fluid. The thermal attenuation is found tobe similar in form to the viscous attenuation and, for gases, of comparablemagnitude. The general results are applied to the case of water drops inair and air bubbles in water.
For water drops in air the viscous and thermal attenuations are camparable;the thermal losses occur almost entirely in the air, the thermaldissipation in the water being negligible. The theoretical values are comparedwith Knudsen's experimental data for fogs and found to agree in orderof magnitude and dependence on frequency. For air bubbles in water the viscouslosses are negligible and the calculated attenuation is almost completelydue to thermal losses occurring in the air inside the bubbles, the thermaldissipation in the water being relatively small. (These results applyonly to non-resonant bubbles whose radius changes but slightly during theacoustic cycle.)
