Hi there,
Welcome to the site!
Head bobbing and arm waving are two things dragons do that they are famous for
Head bobbing is typically a sign of dominance or aggression. And arm waving is a form of submission, or passification.
So what is happening, is your older dragon is aware of the new dragon on his turf, and is showing that this is his territory and that he's the boss around here. The younger one, obviously aware of the size difference, is eager to arm wave to show submission, and show that it's not a threat.
Sometimes them being in site of eachother can stress them both out. So if you notice this, might be best to block their views of eachother.
-Brandon