This is my attempt at an answer to my own question, based upon the helpful responses I have been given so far. I am hoping it may be critiqued until it is correct if it is not already.
The initial condition (set by inflation) is one in which the universe is inhomogeneously filled with baryons, photons and dark matter. The interactions of photons and baryons causes a pressure in this mixture for these two components. The dark matter feels no pressure.
Gravitational forces cause collapse of the baryon-photon gas into over-dense regions. When the density of these regions becomes large, the pressure has increased enough to expel the material out from the region again. This process repeats itself until the time of recombination, where the baryon-photon interactions stop, the pressure decreases and there is only gravitational collapse.
Before recombination, the universe is filled with over-dense regions at all scales surrounded by complicated oscillations of the type described above. For any one of these regions, at recombination the maximum distance a perturbation of the density can have traveled from the source is the distance a sound wave can travel by the time recombination occurs. We can call this L.
In general, a complicated three-dimensional density wave surrounds this region. Simplifying to one dimension, there is a complicated wave with furthest extent just L. A Fourier series may be used to describe this wave (series rather than integral due to the finite extent). Each harmonic of the Fourier series is then a standing wave. The squared coefficients of which are plotted in the CMB power spectrum.