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Theory of Viscous and Thermal Attenuation of Sound by Small Spheres


Carhart, Richard Raymond (1950) Theory of Viscous and Thermal Attenuation of Sound by Small Spheres. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/D77T-8M44.


The problem is to calculate the attenuation of plane sound waves passing through a viscous, heat-conducting fluid containing small spherical inhomogeneities. The attenuation is calculated by evaluating the rate of increase of entropy caused by two irreversible processes: (1) the mechanical work done by the viscous stresses in the presence of velocity gradients, and (2) the flow of heat down the thermal gradients. The method is first applied to a homogeneous fluid with no spheres and shown to give the classical Stokes-Kirchhoff expressions. The method is then used to calculate the additional viscous and thermal attenuation when small spheres are present. The viscous attenuation agrees with Epstein's result obtained in 1941 for a non-heat-conducting fluid. The thermal attenuation is found to be similar in form to the viscous attenuation and, for gases, of comparable magnitude. The general results are applied to the case of water drops in air 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 thermal dissipation in the water being negligible. The theoretical values are compared with Knudsen's experimental data for fogs and found to agree in order of magnitude and dependence on frequency. For air bubbles in water the viscous losses are negligible and the calculated attenuation is almost completely due to thermal losses occurring in the air inside the bubbles, the thermal dissipation in the water being relatively small. (These results apply only to non-resonant bubbles whose radius changes but slightly during the acoustic cycle.)

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:(Physics and Mathematics)
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Physics
Minor Option:Mathematics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Epstein, Paul Sophus
Thesis Committee:
  • Unknown, Unknown
Defense Date:1 January 1950
Record Number:CaltechTHESIS:12112014-103030257
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:8740
Deposited On:11 Dec 2014 20:41
Last Modified:31 Mar 2023 17:43

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