recently I changed 4 tires and the front right-hand-side wheel hub.
After that a strange sound appeared that resembled driving with
off-road tires mounted. That's why I first thought that the tires
are responsible for that. However, today I discovered that the
sound exists even if the car is on the jacks :(
The sound exists all the time the wheels are moving regardless
of Drive/Overdrive/2/1/Neutral position of the gearbox switch.
When I hit the brakes it becomes less loud and remains like that
until I release the brake pedal.
At the moment, for me it looks like the problem comes from the tranny.
However, I have no idea how the new hub (not speaking about new tires) could affect anything in the tranny.
The gears switch smoothly, there is no slipping, error codes whatsoever
but the sound is really annoying.

Thank you for the ideas

I listened to the sound again - perhaps, it's coming from the
new wheel hub and not from the tranny...

Make sure the splined shaft got fully seated in the hub before the big nut got torqued down...otherwise the shaft may be compressed or running out of whack and causing noise...

if what there don't work i wanted to know if you ever got stuck in mud or snow? if so those tranny's are not tuff i know by exsperiance.