I have a 2007 Hyundai Santa Fe that has a very slight back and forth motion in the steering wheel. Hardly noticeable by the eye but can feel it in my hands. Usually at speeds between 20 and 50 MPH and on a good black top road.
When was the last time that the tires were balanced and/or rotated?
More than likely, simply having the tires dynamically balanced will alleviate the problem, but if the tires are overdue for rotation, you should have that done at the same time.
If the problem doesn’t go away after balancing and/or rotating the tires, then it is important to have the front end components inspected. Excessively-worn tie rod ends or ball joints could produce this symptom, and excess wear of those components is a major safety issue.
I used to get that when I was having a bulge developing in my front tires.
99.997% of the time that’s caused by
an out of balance tire,
a bent rim,
a defective or damaged tire,
worn suspension components,
or irregular tire wear caused by one of the preceding choices.
You’ll need to visit a shop to find out which one(s) it is, however you can look at the tire wear charts that Iinked in and see if your wear matches any of the abnormal wear illustrations. Your tire wear can tell you a lot. Post back with the results.
another vote for bulge on tire tread
It can also be caused by a belt that is delaminating under the tread. You may not be able to see this, but you can feel it. It usually does not occur until the tread is pretty low and it occurred more often in tires made 20-30 years ago. I haven’t seen it lately.