In this paper we set out the mathematical problem for calculating the sound waves generated by a MHz voltage - the ESA effect - for a saturated filtration membrane. Three asymptotic solutions are derived, to help build up an understanding of the physical processes involved, and these solutions are then compared with numerical solutions to the full problem. We illustrate the effect of various parameters on the ESA spectra and discuss the problem of extracting membrane properties from ESA measurements. (C) 2012 Elsevier B. V. All rights reserved.