From first principles a general (nonlinear) differential equation is derived, applicable to acoustic propagation in an arbitrary fluid medium. This general dynamical equation is then formally solved exactly, where the medium may include (surface, bottom) boundaries, turbulence, body forces, dissipation, and other physical conditions known to affect propagation. Because the medium is basically stochastic, one must consider in addition the ensemble (or set) of the above dynamical equations, which together constitute the fundamental Langevin (or stochastic) equation governing propagation here. It is then the statistics, namely the moments, probability densities, etc., of the resultant random pressure field, obtained from the corresponding ensemble of dynamical solutions generated here, which represent the ultimately desired solutions of the governing Langevin equation. In the present paper only dynamical solutions are derived; (later, in Parts II and III, stochastic solutions will be obtained from the former). Among the new results obtained in Part I, in addition to the general dynamical solutions, it is shown how the many forms of the ’’wave equation,’’ in past and current usage, are particular approximations of the general dynamical equation derived above, and what specific dynamical conditions must be quantitatively obeyed for the various approximate forms to be valid in applications.