We consider a transmission problem for the propagation of an acoustic wave in heterogeneous media in time-harmonic regime. The domain of interest represents the sun and its atmosphere. This problem involves a large parameter $\alpha$ which corresponds to the exponential decay rate of the density inside the atmosphere. In this framework a boundary layer phenomenon occurs inside the atmosphere. There are several similarities with the skin effect in electromagnetism. We describe the boundary layer phenomenon with a multi-scale expansion in power series of $\alpha −1$. As an application we derive approximate boundary conditions. This approach leads to solve only equations set inside the sun. Numerical results illustrate the accuracy of the approximate models.