You don't mention how many miles the car has done so it's unclear whether the gearbox could be failing - although these boxes are generally strong if well looked after. Is it definitely the box? It could be a wheel bearing. If you're sure it's the box, start by checking the fluid level.

One of our readers also adds that whine may be the intermediate bearing on the longer drive shaft. 'They deteriorate fast from a slight whine at low speed completely masked as speed builds up and then throw off as the bearing disintegrates and creates sufficient clearance for the shaft to exit the gearbox. Fortunately mine (at around 50,000 miles and 5 years old) didn't do any further damage but of course left a lot of oil on the road and was an expensive tow in job to repair.'