good suggestions so far, but from your description I dont think its coming from inside the engine itself. my bet is external.... Sham and CSP thinking its related to the exhaust sounds like a good place to start.
but my suggestion is either the accessory belt itself, one of the pulleys, or the alternator. the reason I say that is because the noise seems to happen when the car is trying to develop electric current (ie demand on the alternator increases).
when the car firsts starts, it puts more demand on the alternator.... noise comes.
when the car has been sitting at idle for a bit (like at traffic lights), its going to have current demand the second you accelerate.... noise comes.
but once you're up and running (and there's plenty of current flowing around), it doesnt necessaryily need that instant juice on the occasional stab on the accelerator when you are already moving at speed.... noise doesnt always come.
a good rule with problems on cars is that if its constant- its mechanical. if its intermitent- its electrical. of course this rule doesnt apply to all sceanrios, but its a good place to start. but I really dont think its the engine itself mate.