Analysis of marginal stability conditions for L_cav = 2 cm, and for a duct of length L_d = 30 cm without side holes. (a) The modulus and phase of Z_load (black lines) and Z_ma (grey lines) are plotted as functions of the frequency. The modulus of Z_sum = Z_ma + (1 − Γ₀) Z_load is also plotted as a function of the frequency, either for Γ₀ = 1.02 (red line) or for Γ₀ = 2 (blue line). (b) The frequency f_r and the growth rate σ are plotted as functions of the feedback gain Γ₀ for the first (red line) and the second (blue line) modes of the system.