The hawk in my video seems to sway with the music. I think it may be a red-tailed hawk.
"The Red-tailed Hawk has a thrilling, raspy scream that sounds exactly like a raptor should sound. At least, that’s what Hollywood directors seem to think. Whenever a hawk or eagle appears onscreen, no matter what species, the shrill cry on the soundtrack is almost always a red-tailed hawk." The Cornell Lab.