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The last few times I started my 86 coupe, I heard static from the rear speakers. It is more of a crackle than static, and stops within 20 seconds or so, or if I turn the radio off (original was replaced with a Kenwood by previous owner). If I get on the gas hard, the static returns for 10-15 seconds and then goes away again.
Does my amp need replacing or could this be a problem from another source like the plug wires, Battery Ground, etc.? I have ruled out a speaker problem, and the fronts work fine. Could the Kenwood have fryed the amp?
From your description it sounds like something external to the unit. Maybe an in-line (12 volt line to the radio) filter will fix it. Available from Radio Shack. It's strange that it only comes from the back speakers, but with aftermarket unit it's worth a try.