This paper discusses the nature of the low-frequency seismo-acoustic waves generated by submarine earthquakes in the ocean. In a finite-depth homogeneous ocean over a semi-infinite solid crust, the derivation of the acoustic equations shows that waves propagate as modes. The waves propagating with the speed of sound in water (T waves) are preceded by waves with frequencies below the Airy phase. Furthermore, the group speeds of these modes are sensitive to the environmental setting. As a test, we applied the spectral finite-element code SPECFEM2D in a simplified configuration with an ocean layer overlaying a solid crust, and a seismic source below a Gaussian seamount surrounded by a flat seafloor. The simulations confirm that the generated T waves and their precursors follow the theoretical dispersion curves. A more realistic environment with a seismically-layered crust and a sound-speed profile in the ocean is then used to predict the expected acoustic modes. Although noisy, recordings by ocean bottom seismometers from the southwest Indian Ocean show T waves preceded by ultra-low frequency waves, which display two modes comparable to the theoretical ones. They are in good agreement for mode 1, whereas, for mode 0, a slight offset in frequency has yet to be explained.