Could be one or all of these items.
Oil level too low- you'll notice 3rd is much higher than 2 and takes you right up to 50 mph or more, this increased speed in the gears can cause starvation of oil to the lower end of the gears.
Bearings worn or damaged. How old are they?
Gear teeth worn or damaged. again, they should be quite old at this point.
The noise is due to bad gears or bearings in your rear differential.
Going to the garage to get new brakes before you gear box goes
Check the fluid level in the trans, the whining is probably the input shaft gear mangling itself.
* If it is stiff and making a crunching noise when going into gear it means the syncromesh (which is the cogs between gear cogs are worn), If it is making a whining noise in first gear it's a flywheel in the clutch, if it makes a whistling noise while travelling the clutch needs replacing, failing all that the gearbox needs grease or your elbow does.
Transmission is low of lube.
Friction in the transmission system may cause whining noise when a car is accelerating. A poor engine or clutch assembly may cause the excess friction in the transmission system.
Third gear could have a broken tooth, chipped tooth or bent tooth on the gear and only makes a noise when it has drive pressure applied to it, so either way when pressure is applied it makes a noise.
The torque converter might be going. but first check your fluid level.
mine whines a different noise in every gear, but it will not whine when i push in the clutch, so i changed my slave cylinder and clutch and the whining noise stopped.
its the pinion gear usually happens when the Axel assembly . is low on fluid, or from hi mileage usage, ether replace the Axel assembly .the Axel bearings get hot and start whining. thanks
To stop a standard transmission from grinding into third gear, check the level of the transmission fluid. If the noise continues, consult a mechanic.
the whining comes from the gears in the transfercase. The gears are larger and smaller dependin on what range your in and the noise is typical notice the rpm to whine ratio, however if the noise is extremely noticeable you may want to check the gear oil in the tcase it may be low. The more the gears become worn the louder the whine will become. Just as a manual trans. is the same.