# Is BAO a standing or moving wave?

The sound horizon is the distance that a wave of plasma can move from the end of Inflation to Recombination (roughly 300,000 years). In several papers and talks, this is described as a moving wave (see https://www.youtube.com/watch?v=JSqIBRbQmb0 at the 23 minute mark). The velocity of the wave is given as $v_{sound} = \frac {c}{\sqrt {3}}$. When recombination occurs, the driving pressure disappears and the density of energy is frozen at that location and is observed by us as a slightly higher temperature than average (the sound horizon).

However, other papers I've read (see http://www.quantumfieldtheory.info/CMB.pdf) talk about standing waves where the sound horizon is a function of the fundamental frequency and the second and third peaks are harmonics of that fundamental frequency. How do I resolve the image of a wave moving down the length of a rope vs. a standing wave on the rope? Is the first peak of the Temperature Power Spectrum associated with a shockwave moving outward from the over-density (as described by Eisenstein) or is it a collapse of baryons inward towards the over-density (as described by Klauber)?

Note that there isn't really a physical different between a traveling and standing wave, except that in the latter case, the position of nodes remain fixed in space --- caused by the interference of different components.

The BAO is not a standing wave. BAO is the product of waves produced by perturbations in the initial matter-energy power spectrum, which traveled/propagated outwards until recombination at which time the waves were 'frozen in' --- i.e. not waves anymore, but the lasting effects of them. Eisenstein's explanation is the correct one (as would be expected for arguably the single largest contributor to the field). Still, the statement "collapse of baryons inward towards the over-density" is also correct, describing the non-linear growth of perturbations --- but that's separate from the BAO 'waves' themselves.