High-resolution direct numerical simulations have shown the occurrence of inertia gravity waves simultaneously with baroclinic instabilities within a differentially heated rotating annulus, the "baroclinic cavity". The working fluid is characterised by a Prandtl number Pr = 16. A decomposition technique applied to the dependent variables has allowed us to separate in space and in time the contributions of the large-scale baroclinic structures from that of the small-scale fluctuations. These latter have been identified as inertia gravity waves from their dispersion relation. The present work is particularly focused on the mechanism responsible for the spontaneous generation of these waves.