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[jdmay]

I've heard that if the wires are too close the there can be a noise like you're having. The manual that came with my amp said to insulate each wire if the amp is making a whining noise. If its only doing when the car's on it might mean that the amp's not getting enough power because of all the other eletrical sytems in the car. That's just a guess though.
I found this at Crutchfield it might help:
Are you hearing engine noise?
Any amp installation can be prone to engine noise. You may hear a whining or clicking sound (its pitch will vary with engine speed). Since most noise problems come from a poor ground, always make sure your ground wire is connected firmly to bare metal in the event of a noise problem. You can also try isolating your amp from the chassis of your vehicle by mounting it on a board or using rubber grommets or feet; using a different brand of patch cables; or, only if all else fails, installing a noise suppressor (like PAC's ANS-80). The tricky part is figuring out which step or steps to take. Please read the rest of this section and try some of the simple tests.

Noise in the patch cables
Noise can be picked up by the RCA patch cables connecting your components. To test this, detach the cables from your amp. (Note: A small number of amplifiers mute themselves when patch cables are removed. To defeat the automatic mute, insert one side (left or right) of a spare patch cable into the amp's left and right input jacks.) Turn on your system and engine. If the noise is gone, reconnect the cables to the amp, and disconnect them from your receiver. If you hear the noise, your patch cables are definitely picking it up. Try re-routing them, taking care to separate them from your power cable by at least 18 inches. Also, newer cars may have a cable that provides power to computers and lights in the rear of the vehicle — make sure that your patch cables aren't too close to this cable.