Shaking issue at highway speeds

Hi guys, i've got a 1999 acura 3.2 TL with 172,000 miles. Just bought it from a guy that has maintained it very well and im quite happy with it.
The only issue that seems to be bothering me right now is that when im
driving above 50 or so, the steering wheel shakes a bit like its not aligned or something is off balance. Occasionally it doesnt shake at all... very smooth. I drove on the same road a couple times to make sure its not a fluke and most of the time, it shakes, but once in a while it doesnt, so its not road conditions. I have a pretty sensitive feel when driving so I definately notice the difference, but people in the passenger seat probably dont. What could be the possible cause, where do I start to look first? (Cheapest to Most expensive options) I'm a DIY guy and i've got alot of experience with auto body work, but not with motors, electrical, and suspension.
Another issue is at above 40 miles the rear starts humming, a bit louder than i'd like, is it okay to keep driving for a while? i'm not sure if its the right side or the left but im pretty sure its the rear. My friend told me its the rear wheel bearings/hub. How do I Test that?
Thanks everyone.
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Does it hum and shake at the same time? Could be a bad tire doing both.

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No, I changed the tires, I dont believe its a bad tire.
Art wrote:

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elus1v wrote:

    Be sure the tire is on the rim corectly and in balance. Check ball joints and steering linkage for play. bob
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As on my TL-S, I have directional tires. Are you sure you do not have a left on the right or vice-versa? Does sound like a tire issue.
elus1v wrote:

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elus1v wrote:

suspension. if you have a shock out, that'll do it. same for a bushing or wheel bearing. make sure wheels are properly mounted, not bent or dented, and torqued correctly.
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what do you mean "shock out" ?
jim beam wrote:

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elus1v wrote:

shock absorber not functioning correctly. like light out.

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elus1v wrote:

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