Wheel bearings.
Check you tube videos of wheel bearing inspection.
If they are bad that is how they start, once they fail enough that grinding, humming... noise will be heard driving straight not just at a slight turn.

Could be something else but that's a start.

 

have you checked your power steering? One persons rumble could be another persons whine. I say this as I have a power steering issue which is only evident when turning. Lift the bonnet and touch the power steering. From what I can gather you shouldn't feel or hear any obvious knocking or vibration.