Based on the acousto-optic effect, transmission matrix method, and planar angular spectral expansion theory, the transmission model of Laguerre-Gaussian (LG) beams in an acousto-optically coupled coaxial atmospheric medium is established,and the acoustic field is used to change the refractive index of the atmospheric medium. Furthermore, effects of different acoustic frequencies and topological charges on the transmission characteristics of LG beams are investigated. Results show that the refractive index of the atmospheric medium is periodically and uniformly distributed after the plane acoustic field is perturbed,and the refractive index stratification period varies for different acoustic source frequencies. The phase distribution of the p-wave always appears on the central axis when LG beam transfers in the layered atmospheric medium. The phase distributions of the s-wave of the incident and transmitted fields remain the same and rotate from the center to the surroundings. The rotational direction of the s-wave phase and p-wave phase are opposite when the topological load of LG beam is opposite, and the phase distribution of p-wave changes. Different acoustic wave frequencies lead to varying refractive index distribution cycles in the transmission path of the LG beam, thereby affecting the phase characteristics of LG beam transmission in the layered medium generated by the acoustic field perturbation. Research results in this paper provide theoretical support for future experimental investigations into the impact of the acoustic field on the transmission characteristics of vortex light.