Sounds like it could be a wheel bearing. Depending on which side it's on, it can become louder when you turn. The wheel on the side of the car that's furthest from the center of the turn (the right side, in your case), needs to spin faster than the wheel on the inside. Bad wheel bearings are most obvious in this sort of situation. 

You can get a noise finder like Scotty uses to find weird noises in cars and hook it up to different areas of the truck to track it down. Depending on how progressed the wear on the bearings is, they may or may not show any kind of play if you jack it up and pull on the wheels. They also may or may not make noise when you spin the wheel. Not having a 4x4 will make this much easier to find the source of the sound. 

This is less likely but check your differential as well. If there's been a leak back there that you've either neglected or haven't noticed, you might be getting low on differential oil, and will want to put some in ASAP. Rear ends tend to bind up in turns with little or no lubricant and can cause grinding sounds.