It could be badly out of balance, or it could have a "flat spot" from broken cords inside the tire. And it may not be the tire at all - it could be suspension system parts.
suspension
It is called friction Out of balance. More weight on one part of the tire than another.
Driving on low tire pressure flexes the tire, causes overheating and can make the tire come off the rim on corners.
the tire will bounce
the friction between the tire & the surface your driving on causes heat and which heats the tire + the air...
Could be a bearing going bad.
latex in the material causes rubber to bounce
Worn steering parts, worn suspension parts, tires out of balance, out of alignment,
So it will run true and not bounce .
most likely the car's tires are out of alignment, or you have a slack tire.
A tire cupping can be caused by tread being lost. A tire cupping means that it should be replaced as soon as possible. You do not want a cupping tire to be used while you are driving. Air can escape and cause a flat.
You may have a rear tire out of balance.