My car makes a funny sound (like an audio cassette being rewound in the area above the radio in the dash) when I start it, and the sound only stops when I turn the headlights on.
I am not very savvy about cars, so simplified advice would be wonderful. Thanks 
Telling us about the car–make, model, model year, odometer mileage–is always a good way to start if you want good advice.
Also–is the HVAC system “on” when you hear this noise?
It’d also be nice to know if you’re the original owner and is so is this a new sound or one that’s always been there.
Also–is the noise–or the absence of it–temperature dependent?
In other words, do you hear it only when the ambient temp is low, or only when it is high, or under all temperature conditions?