The brief
The A4 had a grinding or humming noise coming from a wheel, the kind that builds with road speed and changes with cornering load, and the owner had it pinned to one corner by ear. He brought it in. That noise is the signature of a worn wheel bearing. The bearing lets the wheel spin freely while carrying the weight of the car at that corner, and as it wears the rolling surfaces roughen, which is the hum turning to a grind, and the noise rises with speed because the bearing is turning faster and working harder. A bearing making that noise has run its course, and left long enough it gets play at the hub and can bind, so it isn't something to leave.
The diagnosis
On the lift the wheel on the noisy side spun with a clear gritty resistance and a small amount of play at the hub, the play you don't want, while the others felt smooth. So it was the bearing, confirmed. That's a replacement on the affected corner. A worn wheel bearing only gets worse, and you don't want play at the hub at speed, so it was getting changed.
The work
The brake calliper and disc came off, the old hub bearing assembly was unbolted and lifted away, and a new genuine Audi-spec hub bearing unit bolted on in its place, the axle bolt torqued to spec and the brakes reassembled. The hub was turned by hand to confirm it ran smooth and silent before the wheel went back on. A road test confirmed the noise was gone, smooth at every speed and through corners both ways, with no play at the hub.
The outcome
Noise gone, smooth at every speed, no grind in the corners, and no play at the hub. The A4 went home quiet again. A wheel bearing gives you a good warning before it lets go, so acting on the noise meant a straightforward swap rather than a wheel problem at speed.