High pitch noise from speakers after wideband install. Wideband hooked up to the cigarette lighter wires

 

You should rewire the ground wire. Ground it to the chassis in the car, ideally the chassis itself, but the metal behind the dash will work. This should not only fix the whine, but will make your wideband more accurate.

 

I think that might be a little b/s. A new ground won't make the wide band more accurate unless the cigarette lighter ground is absolutely terrible.

Right on the grounding to the chassis of the car though. Usually that is a better ground. Also while you're doing that also you should just solder the power wire to the ACC wire in the ignition harness instead.

By doing both of these you might get rid of a ground loop. And possibly radiated noise from the power wire getting near your speaker wire.

 

If his cigarette lighter ground is so bad that's he can hear it in the speakers, then yes it will make his wideband more accurate as it uses ground for a reference (same line of thinking as an engine bay grounding kit and why grounding directly to the chassis is better). It may or may not be enough to make any significant difference though.