Hello Ian,
4th gear is direct, with no load passing through the gars. so it invariably will be the quietest.
1st, 2nd, and 3rd are indirect gears, so the whine is probably worn gear teeth. Since the bike probably spend little time in 1st gear, they are probably in the best condition. I have seen the teeth become extremely worn, likely due to poor lubrication. Either lack of periodic lubrication or using straight grease in the gearbox, which when cold and stiff just gets shoved aside. Even in good condition, these gearboxes do tend to whine a little in the indirect gears.
Unfortunate there is not much that can be done about the worn teeth, other than looking for another, better used set. There are not a vast number of the gearboxes in existence, so it may take a while to find such. Be advised that the earlier 4-speed gearboxes from the thirties used a different gear tooth form. Do not mix them with the latter gear tooth form or you will really here a loud whine!
-Doug
