According to Archimedes principle, the weight of an immersed object is reduced by the weight of fluid it displaces. This holds for a fluid parcel of density  surrounded by an ambient fluid of density . Its weight per unit volume is , in which  is the acceleration of gravity. Dividing by a characteristic density, , gives the definition of the reduced gravity:
If ,  is positive though generally much smaller than . Because water is much more dense than air, the displacement of water by air from a surface gravity wave feels nearly the full force of gravity (). The displacement of the thermocline of a lake, which separates warmer surface from cooler deep water, feels the buoyancy force expressed through the reduced gravity. For example, the density difference between ice water and room temperature water is 0.002 the characteristic density of water. So the reduced gravity is 0.2% that of gravity. It is for this reason that internal waves move in slow-motion relative to surface waves.
Whereas the reduced gravity is the key variable describing buoyancy for interfacial internal waves, a different quantity is used to describe buoyancy in continuously stratified fluid whose density varies with height as . Suppose a water column is in hydrostatic equilibrium and a small parcel of fluid with density  is displaced vertically by a small distance . The buoyant restoring force results in a vertical acceleration, given by
This is the spring equation whose solution predicts oscillatory vertical displacement about  in time about with frequency given by the buoyancy frequency:
The above argument can be generalized to predict the frequency, , of a fluid parcel that oscillates along a line at an angle  to the vertical:
This is one way to write the dispersion relation for internal waves whose lines of constant phase lie at an angle  to the vertical. In particular, this shows that the buoyancy frequency is an upper limit of allowed internal wave frequencies.