Electromagnetic Gaussian beams may be described by using a Davis scheme of approximations. It is demonstrated that this scheme also may be used, with minor changes, to manage the description of acoustical waves. The acoustical version of the Davis scheme afterward allows one to establish an efficient and accurate localized approximation to evaluate beam shape coefficients, which encode the structures of acoustical waves, similar to the localized approximation, which has been made famous when dealing with electromagnetic waves. The present paper is restricted to the case of on-axis beams.

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