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I test drove an 87 today and I tried out the radio controls just to make sure things were working properly. The radio sound OK and when I turn it off the antenna goes all the way down. So far so good...
Once I turn the radio off, I hear a whine from the speakers that changes in pitch and volume with engine RPM. As soon as I turn the radio on, the whine nearly disappears. Actually, at the lowest volume setting, I can not really make out any whine at all. If I get this car, it will be used mostly for autocross and track use, so any big radio problem is not really a deal killer.
Each speaker has its own amplifier and the radio on/off switch activates a relay to supply power to the amplifiers. When the radio is off, then the amplifiers should also be off and no audio should be possible from your speakers. I would check for stuck relay contacts or a bad radio on/off switch.
On mine it sounds like the left front amp/speaker is the problem. Right now it seems to only do this after shutting the motor off.
Now that I own the car, I have noticed that when I start the car up in the morning, there is no noise. Is this because of some sort of voltage bleed-off and the amp relay won't see any power until the radio is turned on? I normally leave the radio on, but I tried turning it off before engine shutdown to see what it would do in the morning.