What determines the frequency of the wave at the coffee/milk boundary of my iced coffee? As I set down my iced coffee, which I made by first pouring a bit of milk over ice, then adding hot coffee over ice without stirring, I noticed that the jolt of setting down the glass had set up a wave in the stratified drink at the milk/coffee boundary. This wave had a relaxingly long period of nearly 2 seconds.
I was surprised at how slow this was, given the small volume and diameter of the glass.
What are the relevant parameters that govern this phenomenon? I imagine perhaps the density differential between the milk and coffee, plus the damping effect of the ice on fluid movement. What would the relevant equations be if we ignore the ice?

 A: These are obviously gravity waves. They are often derived for the interface between water and air (sea waves). Since the density difference between water and air is much more pronounced than in your example, water waves have smaller wave lengths/higher eigen frequencies in closed vessels.
Note that gravity waves can also be viewed as a result of buoyancy: the valleys are partial cavities that experience upthrust relative to the surrounding hills. And as always with buoyancy, it is the density difference that determines the magnitude of the resulting force. For the milk/coffee boundary, a "coffee valley" next to a "milk hill" experiences only a small buoyant force, and hence the milk/coffee waves have "smaller frequency" (or rather smaller wave velocity I should say), if we neglect the effect of inertia.
The fact that it has to be gravity which is responsible for the phenomenon, is visible from the fact that the milk settles below the coffee, so it has to be denser (which someone might be able to explain from the chemical composition of milk/coffee and/or the thermal expansion of both), which does invariably lead to such waves.
Note several caveats:

*

*gravity waves are only simple to understand for small amplitudes (linear approximation); this is more of an issue for sea waves, whose amplitude is very often so high that they tumble over (which violates the linear approximation); for the milk coffee this is less likely, just because the densities between both constituents are so similar, and probably also because of higher viscosity compared to air

*the gravity wave treatment requires a defined surface, which is not the case for milk/coffee because they are miscible; the mixing transition between milk and coffee would complicate the mathematical treatment considerably (especially given that there is also free thermal convection, which also determines how they mix, locally)

*generally, waves at interfaces are also somehow determined by surface tension (i.e. a non-gravitational force); however, the effects of surface tension are usually only significant for pretty small curvatures/droplets; and I doubt that this plays a role in your experiment (otherwise you would likely observe big blobs of milk or coffee sometimes); but a popular counterexample are "lava lamps", the famous "relaxation paraphernalia" of the 1970s and 1990s: the densities of both fluids are very close together, but you can also see blobs, which rise again due to free convection, and which are dominated by surface tension waves.

