the whine matches the rpms because a bad ground or a grounding of your antena is letting feedback from teh ignition interfere with your radio.
on mine the ruber had deteriorated at the base of hte antena and the part that should have been insulated was ocasionally finding a ground. when it did I had static that changed with the rpms. if I'd hit a bump or slam a door it would change, it was simply breaking the ground.
yours could be the antena, or a bad ground in the power for the stereo.
as to were to look. other than the obviose (where the antena wire plugs into the stereo or antena, and if the antena is mounted properly and in good condition. or wire conections from the stereo to the harness) it could be anywhere.
good luck hope you find it easy. one thing to help is to notice all of the things that change it (like the door thing you mentioned), and try and use them as clues to narrow down where it could be that all of the clues would have an effect on.