If the wheel has been professionally trued, that should not be the problem. You can easily check this yourself; just put a finger very close to the rim and give 'er a spin. There should be no more than 1mm of side-to-side play. Likewise check for roundness.

Possible things to check might include a badly-manufactured tire. Does the wheel seem unbalanced? If spun, it should naturally end up with the stem side down. If it doesn't, there may be a "thick spot" or other defect.
Hub-bearing failure? Does the wheel spin freely and without any crunching side-to-side play?
Frame/wheel alignment problems will normally just cause pulling or bad tracking; if things were really "out" it might cause a wobble sensation.

It sounds like loose spokes to me; but if the wheel has been properly trued that shouldn't be the problem.
Wouldn't hurt to give them all a little tap with a wrench and see if you get a similar tone from each.