### ASA 124th Meeting New Orleans 1992 October

## 3pSA11. Modal surface impedances for two spheres in a thermoviscous
acoustic medium.

**Mohamad Hasheminejad
**

**
Thomas L. Geers
**

**
**
*Ctr. for Acoust., Mech. and Mater., Dept. of Mech. Eng., Univ. of
Colorado, Boulder, CO 80309-0427
*

*
*
Two spherical bodies are submerged in an infinite thermoviscous fluid; one
body is motionless and the other is vibrating at high frequency with a surface
pattern that is axisymmetric with respect to the line joining the centers of
the two spheres. Both bodies are sufficiently good conductors that their
surface temperatures deviate insignificantly from the ambient temperature. The
acoustic stress and velocity fields on the vibrating surface may be
conveniently related by a modal surface impedance matrix based on field
expansions in Legendre functions. This impedance matrix, which of course
accounts for the presence of the motionless sphere, is here obtained from the
field equations of Epstein and Carhart [J. Acoust. Soc. Am. 25, 553--565
(1953)] through the application of translational addition theorems for
bispherical coordinates [Y. A. Ivanov, Diffraction of Electromagnetic Waves on
Two Bodies, NASA Tech. Trans. F-597 (1970)]. Impedance matrices for fluids that
exhibit thermoviscous boundary layers of various thicknesses are compared with
counterparts produced by the thin-boundary-layer model [A. D. Pierce, Acoustics
(McGraw-Hill, New York, 1981)]. Special attention is devoted to the case when
the motionless sphere is sufficiently large relative to the vibrating sphere
that it approximates a rigid wall.