When coupled to acoustics, unsteady heat release oscillations may cause recurrent problems in many combustion chambers, potentially leading to dramatic damages to the structure. Accumulation of acoustic energy around the eigenmodes of the combustor results from the resonant coupling between pressure disturbances in the flame region with synchronized heat release rate perturbations. Predicting these frequencies and the corresponding sound pressure field is a key issue to design passive or active control systems to prevent the growth of these instabilities. In this study, an acoustically controlled combustion test bench CESAM is used to stabilize a partially premixed swirling propane-air flame. In the premixing tube, reactants are injected tangentially to generate the swirling flow, the flame being stabilized in the combustion chamber by a sudden expansion of the cross section. The premixer backplane is equipped with an Impedance Control System (ICS) allowing to adjust the acoustic reflection coefficient at this location. Acoustics of the coupled-cavitiy system formed by the premixer and the combustion chamber is investigated analytically by taking into account the measured acoustic impedances at the premixer backplane and in the feeding lines. The chamber length is also modified to examine effects of the geometry on these predictions. It is shown that the premixer and combustion chamber can be considered as acoustically decoupled for small values of the acoustic coupling index, defined in the article, offering flexible solutions to control the pressure distribution within the combustor, except when these frequencies match. When the frequencies are close to each others, only the analysis of the damping of the different cavities enables to indicate wether the system is coupled or not. Modifying either the acoustic coupling index or the damping values featuring the same frequency appears then as alternative solutions to decouple cavities.