Whether it's a back bike wheel wobble or a hop, in the vast majority of cases the problem is caused by the wheel. In a very few cases, it may be the tyre. The first step is therefore to establish whether the problem comes from one or the other.
To find out, check these points in the order given to eliminate the causes one by one:
1 - Check that the tyre is fitted correctly
Some flaws such as those described above may simply be the result of incorrect mounting of the tyre on the wheel seat. This can happen in particular with a tubeless-ready tyre (sometimes also with a tubetype, but it depends on the wheel).
If the tyre is not fully clipped in, the tyre will not be evenly positioned around the wheel, resulting in a bike wheel wobble.
When fitting the tyre, you need to have heard the snap sound when the tyre clicks into place. If this has not happened, there is a good chance that the mounting has not been completed correctly.
To solve this problem, it's very simple: add pressure and the tyre will settle itself. ATTENTION: It is mandatory not to exceed the maximum pressure recommended by the tyre and rim manufacturers. Both are marked on the tyres and rims.
2 - Check the wheel
If it's not an assembly fault, the wobble or hop may come from the wheel or the tyre. As in most cases it is the wheel, we will first look at the steps to follow to confirm this.
Remove the tyre and put the wheel back on the axle (on the chainstay if it's a rear wheel or on the fork if it's a front wheel).