Just changed alternator due to seized bearing and installed new alt and
P.S. belts while I was at it. Car starts and runs fine now but there
is a rattling sound while the car is running that I can not pin point.
(I have been using a plastic tube as a stethascope)

Its in the area of the alternator/P.S. pump/A/C compressor but I don't
believe its any of these items. Also when I shut the car off something
keeps turning (and rattling) for at least 3-4 more seconds (there is
nothing visually moving during this time) Its been many years (and
miles) since the last timing belt/water pump replacement. Could the
water pump be the culprit?

Thanks