About a week ago, my radio developed a lot of static only when my engine is on. No static when the engine is off. I've isolated the problem down to the alternator. When I run the engine and disconnect the alternator from the battery, the radio static goes away.

I ran a multimeter on the battery with the engine off (12.7) and with the engine on (14.4), and it seems as if the alternator is still charging the battery.

Is my alternator going bad and therefore interfering with my radio? Do I need to replace the alternator?