3.8 Impala w/ vibration issue on driver side. Low vibration sound at low speed and gets higher pitched as car speeds up. Has become more noticeable over time. Began at 40K, now at 97K. Steering feels loose as well now.

check your wheel bearings

If a hub bearing was bad, it almost always would make noise, more so when changing lanes at higher speed. Outer CV joints make a loud low pitched rattle when turning (corners). Inner CV joints raise hell at high speed- bad shake! Sway links affect cornering and clunk when hitting rough patches of road surface.
Is the vibration worse at 65 than at 50? If so, you are dealing with a wheel balance situation. Find an old time front end shop that will check the balance on the vehicle. You will have to turn off the traction control to do this or use an on-the-car wheel balancer.
If you feel it at some low speeds at it comes back at other higher speeds, then you are dealing with tire roundness. Possible more than 1. More common than we would like.

this problem could be a worn or loose wheel bearing or a worn or broken shock or a worn tie rod inner or outer.

Did you recently change your tires? An aggresive tread design, like a mud and snow tread, can create road noise that becomes more noticable at higher speeds. Bad wheel bearings can also produce a "roaring" sound, especially in front wheel drive cars. To check them, jack the front wheel up and spin the tire by hand. It won't spin smoth and even, there will be some resistance and you will hear grinding or crunching.

If your transmission was low enough on fluid, it could conceivably make noise. Also check your U joints or CV joints for play. any play in them will make noise although it is usually accompanied by a feeling of looseness or "jerking", especially when making changes in direction or speed.

There can be a lot of reasons for noise, but start by checking these things first. Hope this helps.

You need wheel bearings.. One for sure maybe 2. Do you feel it in the steering wheel or floor? The floor usually means rear and the steering wheel usually means front. Hope this helps. It should change pitch when you drive left to right at a steady speed. :-) Cobra

ARE ONE OF YOUR WHEELS BENT? OR YOUR TIRES MIGHT BE THE PROBLEM ,YOUR DRIVE SHAFT MAY NEED TO BE BALANCED

this sounds odd but mine did this when i replaced the wipers. it seems the design of the wiper frame was making a whistle at higher speeds. the freestar wipers are exposed on the window cowl and not hidden so they endure the winds at high speed. it is worth a shot.

Could be a U-joint near failure. You will know it is a U-joint if you hear a clunk when you put it in gear. Failing U-joints will cause a lot of vibration just before they go.

Apparently the whine is car speed related and not engine speed. I'm surprised that you didn't say anything about checking the wheel bearings?

A bad tire, a loose wheel, a loose tie rod end, a bent rim, (tire balance at higher speeds), a piece of rust or whatever caught between the rim and brake rotor, or between the brake rotor and hub. Have you done anything to it prior to this starting?

I had this issue and it was one of my winter tires about to blow out, showing signs of weakness.. hopefully this helps!