In numerous industrial systems, acoustic resonances are synonymous with loud noise and dramatic structural vibrations. They take their origin from trapped weak pressure waves, but can sometimes develop into complex instabilities. With specific emphasis on turbomachines applications, two computational methods have been developed for the prediction of acoustic resonances in core volumes. The first method, called the averaged response function, consists of combined time-domain and frequency-domain approaches. A Favre-averaged RANS solver is used to model the response of a system to a controlled chirp excitation. The response is then analysed using well-known modal analysis tools in order to extract the system’s acoustic characteristics. The second method, called the Arnoldi method, focuses on the stability of the CFD solver. The system is transformed, using a linear Euler solver, into a classic matrix stability problem. The eigenpairs of the matrix, corresponding to the acoustic modeshapes of the system, are then extracted thanks to the iterative Arnoldi method. The two methods are validated and compared on a wide range of cases such as enclosures, open geometries and flow applications. Such a thorough study first provides the reader with a deeper insight into acoustic phenomena by considering classic acoustic examples such as the end correction concept, the Doppler effect and the ”lock-in“ phenomenon. This study also investigates the limitations and qualities of the implemented methods which are seen to behave very well when compared to theory and experiments. They give accurate results in predicting the three components of the acoustic resonance: the frequency, the damping and the modeshape. As a result, the methods implemented are considered to be mature and can be used to study either the complete acoustic map of the system across a wide range of frequencies or specific acoustic instabilities in a narrow frequency range.