Due to the complexity of sound waves in the atmosphere, the numerical simulation method is widely applied, but the expressions of the analytical solution are not given, and its precision is limited. In this paper, the second-order miniterm approximation acoustic wave equation containing the attenuation and nonlinear effects is solved using the homotopy analysis method (HAM). Firstly, initial approximate solution with attenuation term is introduced, the first, the second approximation solution and the 3rd-order approximation solution are obtained by iterative formula of HAM; and then sound speed profile, wind speed profile, temperature profile of a cloudy windy night are obtained using the Monin-Obukhov similarity theory , and numerical simulation of the approximate solutions is made. Results show that the waveform of the approximate solutions have distortion and the sound pressure decreases with the increase of propagation distance, so it is of great significance to research the sound wave propagation in the atmosphere.
