A shortcoming of widely-used integral methods for prediction of flow-induced sound emission of rotating systems is that the rotation of the impeller can be included in the calculation, but not reflections of sound from the housing, rotor blades and attached ducts. This paper introduces a finite element method that correctly maps both the sound sources rotating with the impeller and the reflections of the sound from the rigid surfaces of the components of the blower. For the prediction of flow-induced sound a hybrid approach is employed using separate CFD and acoustic simulations. It is based on a decomposition of flow (incompressible part) and acoustic (compressible part) quantities and is applicable to high-Reynolds-number and low-Mach-number flows. It features only a scalar unknown (i.e. the acoustic velocity potential), thus reducing the computational effort significantly. In order to compute the sound propagation in the rotating and stationary reference systems simultaneously, a domain decomposition is performed on the numerical model. The rotation of the impeller is introduced through a moving mesh, where the blades act as rigid surfaces. For the exchange of sound waves between the non-conforming meshes of the two disjoint regions the Nitsche method is used. The developed method is then applied to a ducted axial fan in order to identify the flow sound sources. The predicted sound pressure level is found to be in good accordance with measurements. An automatic workflow for evaluation of the quality of CFD data and for identification of relevant sound sources is presented.