Water Pump ????
 

What could cause my water pump to produce a horrible sea lion sound from 1500 to 3000 rpms. The belts brand new but then again so is the water pump. Im thinking maybe theres a little bit of trash but the coolant has also been recently changed. Any ideas?

Improper belt tension, some manner of fluid on the belt causing slippage, or a failed bearing in the waterpump. Screaming bearings is a more common failure mode on American V8s than imports, but no reason it couldn't happen on a Miata. Any leakage at the weep hole?

it might actually be a sea lion, have you looked for one?