〗Small scale atmospheric acoustic wave fluctuations of linear approximations can be described with Helmholtz equation. The Helmholtz equation must be solved in order to analyze the characterization of atmospheric acoustic wave fluctuations. Most of the methods to solve the Helmholtz equation are realized under certain boundary conditions and initial conditions, while boundary conditions and initial conditions are obtained on the basis of assumptions, approximation, and make calculation process complicated and computation amount bigger. Exp function method with many free parameters is a very effective, direct tool to solve precise solutions of the nonlinear problem and the boundary and initial conditions can be neglected，the interaction of exp function and hyperbolic tangent transformation can approximate to linear transformation. In this paper, firstly the arctangent transformation is taken to Helmholtz equation and the equation is transformed into nonlinear equation. Then the single wave solution, double wave solution and three wave solution are assumed and solved. Finally, the Single wave solution, double wave solution and three wave solution are simulated in 3 dimensional spatial and 2 dimensional planar with infrasound and audible acoustic waves. The results show that different frequency acoustic waves have different propagation characteristics; the double wave solution and three wave propagate along the respective direction with non interference each other under linear approximations.
