Whining sound from wheels

SAME AS ABOVE QUESTION: I have a 2001 Ford Crown Victoria Police Interceptor that for many months is making a whining sound from wheels or rear-end when alternating pressure on the gas pedal. No sound with hard acceleration. Not an engine sound. Checked differential oil and it was very low, so we filled it, 30k miles ago. Sound is slightly louder over time/40k miles. I'd like to stop the sound so I can sell the car.
MORE:
Mechanic friend says might be wheel bearing or differential and not to worry about finding it til the problem becomes clear what or where it is. It is mysterious, but the car runs great. I just think it will be hard to sell this way.

Is there a repair I can make or some oil or additive I can add to the differential that will stop the whining sound?

Thanks!