Having busted through many a traffic light going as quickly as possible on my way to the local donut shoppe… I will have to say that we often just used our fingers, not some study, to determine which siren to use.
The average police car has all of the aforementioned sirens in his catalog of sounds and few that he or she may just not use.
Most often, we will switch between one and another, “our favorites”, and then flick the air horn when approaching an intersection. They are most often arrayed as a bank of toggle switches on a small box amongst the thousand other things that a cop must fiddle with while driving (his computer, his heater, the coffee, the fresh donuts, the radio, the radar gun, your partner). You guys think you have distraction issues!
People don’t hear sirens and they don’t hear the horn. So, I just generally did what any law abiding cop would do: yell from my closed windows “GET OUT OF THE WAY YOU MORON!!!” and merrily went on my way.