The reason they turn them off again after they passed the lights is because they don't want to annoy the hell out of people with their siren OR because they don't want to alarm anybody who shouldn't know they are coming!

However, in most areas, it is the law that police officers must have their sirens on when travelling to a crime scene in an emergent fashion. In 99% of the cases where I've seen things similar to the earlier post, they are not moving any faster then the speed limit, indicating that they're not in the rush that running a red light would imply, they're usually doing it because the doughnut shop is about to close (at least in the cases where I've followed them, again, at normal speed). I, personally, haven't seen any of this since our government had video cameras installed in cop cars that turn on when the siren is turned on. You do the math. But if you live in an area where policemen are actually friendly and do their job without hassling people or abusing their power, then count yourself lucky. Those places are becoming harder and harder to find.