Alternator, Battery, Grounds and Speakers

I have a 2000 XJ sport that I've owned for 3 month. I was having problems with the alternator and would have to charge the battery. When I took the alternator out it test good..put it back in and I had no problems. Every once in awhile when i turn the vehicle on the battery gauge only rises about half way and the battery slowly drains until the check gauge light comes on, After the car is warm I will shut it off and turn it back on, then the gauge goes back up? (most of the time)

I checked all the ground I could find and made sure they were tight...Replaced the negative battery cable. They seemed to fix my problem for a little while.

I also think I have a short in my driver side speaker...it hums with the rpms of the engine....Could this be my problem?

Parts store testers have problems testing the Nippondenso alternators that are controlled by the PCM.

I would pull that alternator and take it to a alternator shop, or if you don't have one close by then drive the vehicle into a shop and have them test it on the vehicle.