Why does a car whine in reverse?

When you put a manual car into reverse gear, there's a very definitive 'CLAT' as you clink the gearstick into place. And as you set off and start gathering pace with your arm around the back of the passenger seat, you'll all know that whine the transmission makes that grows as engine speed increases.

Why does the 'R' cog actually make that distinctive wail once up and running? My engineering geekiness is here to enlighten you about the ins and outs of reverse gear!