Internal gravity wave instabilities play a significant role in geophysical fluids, often leading to the creation of time-growing solutions in fluid equations due to nonlinear effects. In our work, we explicitly construct solutions of the Boussinesq equations, linearized around a plane wave, which exhibit exponential growth in time. This growth arises under specific resonance conditions. This research represents a first step in describing the TRI phenomenon. Joint work with Thierry Paul.