I don’t know why it couldn’t be a tire balance problem, which can come and go with varying speeds.
A short time back I was on the turnpike (I usually avoid them) and noticed my car vibrating a little at the 75 MPH posted speed limit. Backing off to 73 and under would smooth it out. The next day I checked the tire balance which showed to be off a bit and all was well after rebalancing them.
There’s also a few unknowns which may never be known unless the OP posts back. This involves keith’s comment about moving the used rears to the front and the always lingering question; was there any lesser vibration leading up to the complaint speed?
People can sometimes be pretty oblivous to noises, vibrations, ride, and performance problems on their vehicles.
A few years back my daughter bought a new set of tires for her car at Wal Mart. Several weeks later she was visiting and circumstances dictated that I go somewhere with her. The minute we hit 30 MPH I could feel something was wrong (not to her) and at 55 the car was bouncing horribly.
Turning around I pulled the 2 rears off and found that one of those new tires (a Goodyear) was 4 ounces (NOT point 4) ouf of balance. (This led to an eventual free tire replacement because 4 ounces on a 195/60/15 is huge.)
She had been driving around for 2 weeks blissfully unaware that the rear end of her car was acting like a dribbled basketball.