Under the combined forces of pressure and gravity, the two modes remain distinct. Figure 2.1 shows the dispersion relation for waves propagating in the vertical direction (i.e., along the z axis). Acoustic waves propagate for ω > ω_{ac}, with group and phase velocity greater and less than the sound speed respectively, and approaching zero and infinity at ω_{ac} respectively. At high frequencies, the waves are purely acoustic. Gravity waves are propagating for ω < ω_{ac}, with phase and group velocity less than the sound speed. For large k_{x}, the waves are purely gravitational. The acoustic cut-off is larger than the Brunt-Väisälä frequency by a factor,

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