Transmission or tires?

I am thinking that the noise is from a failed wheel bearing or possible cv joint failure
find yourself another service dealer as tire noise is either there or not there and rotation (if it is a faulty tyie ) would move to the new position
Here is a clue to consider
rotating tires is a ploy by the tire dealers to sell tires
have a wheel alignment done on the rear first and then the front and leave the tires alone
if it is a front wheel drive vehicle you will get 3 times the mileage out of the rear tires compared to the front drive tires and that is a big saving for you
next point -- radial tires continue to wear in the same pattern regardless of where they are put so how are you to know it it is a faulty tire construction or a need for a wheel alignment
third point --- many brands of tires are made as directional tires ( a directional arrow on the side wall) and cannot be rotated because they cannot be fitted on a wheel that rotates against the arrow
if they are the wear in pattern of the belts in the rubber is altered and may lead to tire failure ---the tread pattern is designed to remove maximum water and produce maximum grip in the direction of the arrow

The noise would be coming from something that is turning at the same speed as the tires.
It could be a hub bearing or a worn tire.

That most likely is a bad wheel bearing my friend. Jack each corner of the front and see if the wheel and tire will "shake" by trying to move the top of the tire in and out. On rear wheel drive vehicles, the rear axel will move in and out or op and down. If you spin the rear tire you may hear the grinding noise. Change that bearing where it moves or is noisy.

Check Tires for feather edge. Join your fingers together, move around the rear Tire from front to back and vice versa on both of the rear Tires and feel the smoothness. If the tread of the Tire resist the fingers in one direction and smooth on the other, then the Tires may be producing the abnormal noise.
Temporarily bring both the front Tires to the rear and rear Tires to the front on the same side, drive the car and watch the noise. If the noise begins to come from the front end, then the Tires are defective and need replacement. . If the noise still comes from the rear wheels then the rear wheel bearings need replacement.(You can also rotate the Tires in criss cross manner temporarily)
The bearings often vary noise with and without load. Be sure to troubleshoot the noise before spending money on costlier spares.

most def you need an alignment and you also need to check inner outer tie rod end and check the tires belt as well

take the wheel out and make cure the Bering wheel is good

If the sound follows vehicle speed and not the engine you could be hearing u joint noise from the Driveline also. Will get progressively louder with speed.

have someone ck the wheel bearings,and ck for poss. vacuum leak at upper to lower intake manifold gaskets

Hub bearing in the right rear is the most likely problem

first check condition of discs and pads if all is good drive and pull up handbrake slowly to see if its the handbrake shoes making the noise if still a problem will most probably be rear wheel bearings