Question about a 97 Elantra

The other day my wife noticed that the car started making a noise and vibrating when it got up to 40mph and continued if she went faster. The tires are good and one thing I noticed and I am not sure if it should be like this or not, but on the front passangers side wheel, when I had the car jacked up the wheel would give a little play. I could push and pull the wheel straight into and from the body just a little bit. Should the wheel be able to move like this? If it is not I wonder if at around 40mph the wheel is starting to vibrate and that is what the problem is. Any ideas??

WSC65 most likely your wheel bearing is fried,I say this because I just replaced the one on my driver side. Its an easy fix if thats what is wrong, you can do most of the labor your self. It consist of removal of the ball joint, tie rod, hub assembly from the strut bar, should take about an hour to remove if you have all of the required tools. The one thing you will have to be done for you will be to have old bearing pressed out at a local shop that has a press. Cost of the bearing should be between $20.00 and $30.00 depending on the store and the labor on removal and replacement of the bearing should'nt be more than $50.00 at the most