Abstract:
Two theoretical topics in support of bubble cloud measurements are presented: (1) Corrections to Foldy's effective medium theory. A very large class of multiple scattering contributions are summed to give a correction to Foldy's formula for the index of refraction of a random collection of small scatterers. The result has a simple theoretical interpretation, and is a much smaller correction than that obtained by [Z. Ye and L. Ding, J. Acoust. Soc. Am. 98, 1629--1636 (1995)] due to cancellations between their multiple scattering contributions and others. The probable effect of neglected contributions is discussed, and contrasted to a claim that Foldy's model gives infinite results [A. S. Sangani, J. Fluid Mech. 232, 221--284 (1991)]. The finiteness is due to a cancellation between multiple scattering terms. (2) The Kramers--Kronig integrals are applied to resonator data. (This work is done in collaboration with R. Goodman, D. Farmer, and S. Vagle.) The real and imaginary parts of the index of refraction are measured, and the Kramers--Kronig integrals give a prediction for each in terms of the other. Discrepancies between the measured and predicted functions indicate inaccuracies of the measurements, if enough bandwidth and fine enough sampling are included.