The water pump should have zero movement, it will be a rumbling sound when the pump goes, the hot water washes out the grease in the bearings eventually just going bang in a big way, so from your description I would say it's the pump, you'll soon tell by taking belt off and spinning, the noise from alternators tends to change with load so putting everything on will alter the noise if a bearing in the alt it will start singing, sound squite good actually!!
tabetha