QUESTION: "I was outside and a State Trooper drove by with siren blaring. It was pretty loud and it got me thinking about what is is like inside the car. Is it loud and annoying to have the siren on if you are driving the car? Is the car soundproofed for trooper hearing protection? Or does the sound cancel out because you are under it and it is moving or some other wonder of physics?"
I entitled the Title like I did in that I was flashing back to a song, some of you will remember, by Simon and Garfunkel's - "The Sound of Silence?"
"Hello darkness, my old friend, Ive come to talk with you again, Because a vision softly creeping, Left its seeds while I was sleeping, And the vision that was planted in my brain Still remains Within the sound of silence ..."
BRIEF:
" Is it loud and annoying to have the siren on if you are driving the car?" No
"Is the car soundproofed for trooper hearing protection?" No
"Or does the sound cancel out because you are under it and it is moving or some other wonder of physics?" Yes and No
Most law enforcement vehicles are equipped with 100/200-watt electronic siren amplifiers and the speakers are mounted on the roof. As you eluded to, it does put the "sound" above and while there is not special insulation in the roof, most vehicles, including yours have an amount of insulation in the roof between the roof liner and outer shell.
Speed of the vehicle is a factor. The slower you go the louder it will be within - the faster you go the lower the sound will be within the cruiser up to and including "The Speed of Sound" where it will become "The Sound of Silence!" Well, maybe not that fast, but it will diminish. IF the cruiser window(s) are down it is louder for sure.
While Law Enforcement Officers can't "outrun" the sound of the siren, they do have to take into consideration that the faster the go that they are closing the gap of YOU being able to hear and perceive that an emergency vehicle is approaching and the Officer's ability to avoid a collision should you not!
Running a siren in a downtown area amplifies the sound in that it echoes off the fronts of the buildings.
Hope that answers your question?
Remember that the law requires that when you hear the sound of a siren and/or see a vehicle displaying flashing red or blue lights, that you pull to the extreme right side of the road and come to a stop, irregardless of the direction you or the emergency vehicle is traveling in. Stay Safe!