Summary of our physical model with finite size interfaces: m convective steps of constant size d and indexed by the integer 1 <n<m, are separated by interfaces of size l. a) General scheme: the incident, reflected and transmitted waves have amplitudes , ℬ₀ and , respectively. In the nth convective step, the ingoing wave has an amplitude , and the outgoing has an amplitude ℬ_n, while in the nth stably stratified interface they have amplitudes and , respectively. b) The corresponding density profile: in each interface, the density follows a gradient , so that the density varies by an ammount Δρ> 0. In the convective steps, it follows an adiabatic gradient. Thus, the mean density gradient , where L = l + d. c) The corresponding buoyancy frequency profiles are N² = 0 in the convective layers and in the interfaces to create the mean stratification .