I would confirm that. It will tell me if it is alternator whine a failure in the radio itself or a combination.
Based on your answers since it does this with the radio off, I believe this to be the amp is on for the chimes since they sound through the speakers. It is either there is a ground loop between the antenna and the ground. Test by ohming between the two. It should measure 0 to several tenths of an ohm. Try disconnecting the antenna and playing a CD or see how it responds when off.
The other 2 possiblites are defect in the amp (likely caps in the input section of the power supply) or other defect. The other option is the radio itself.
i don't know exactly how the info is passed back and forth with the interface to the car, but those are the likely things to look at.
Jeff