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If you are wondering how a mechanical or electronic siren type works, here is some information for you.
I'm only explaining mechanical and electronic types because they're the only types of sirens that exist.

Moving on to mechanical sirens:
a mechanical siren is basically a siren that uses very rapid bursts of air to create a smooth tone. To put it into contrast, think of saying the letter "R" fast and constantly. What you'll notice is that when you say it slowly, the "R" sound is composed of tiny air-bursts of your tongue flapping back and forth. And the faster you do that, you'll notice the smoother the "R" sound becomes. That's the main principle behind the working of a mechanical siren; only a siren uses impellers or disks that spin.
About the impeller method: first of all, for those of you who do not know what an impeller is, it is a type of fan which sucks in air from the front and expells it out through the sides. In the case of a mechanical siren, the impeller, also known as a rotor or chopper, is covered by a slotted drum, known as a stator. Both the impeller and stator have slots; both with the same number. As the impeller spins, it sucks in the air and tries to push it out through the stator ports. But because both the chopper and stator have the same amount of slots, as the slots of the impeller close the stator ports, the air gets compressed; and when the impeller openings do align with the stator openings, the air gets pushed out in a burst; hence how I told you that saying the letter "R" continuously makes a smooth tone; and when slowly, you can hear the bursts that make up the letter. So a burst from the impeller is like a flap of the tongue. So as the impeller spins faster, the more of those bursts happen per second; and the smoother the tone gets, meaning that the seperate bursts are not recognizeable, but a smooth tone is heard. Also, the faster the impeller spins, the higher the pitch, due to more air bursts per second.
I've told you before in this post, that there is not only that method to a mechanical siren; there is also the disk method, too.
How the disk method works is on the same principle as the impeller/stator assembely; only this time it's two disks: one disk spinning- the chopper, under a stationary disk- acting as the stator.
Now, since this involves a spining disk, there is no suction power on a disk as there is in an impeller, to push it out through the stator ports. So, because you cannot push the air through the stator with a disk, you need a compressor to push the air for you. When the compressor pumps the air to the chopper disk, the disk spins. As it spins, its holes will, at one moment, align with the holes of the stationary disk. As the holes align, the compressed air will flow out the holes for a second, and make a burst. And as that spinning disk spins under the stator disk very fast, those short bursts of air will make a smooth sound.
Here is some general information on chopper/stator sets: in order to make those bursts of air seem like a smooth noise, the chopper has to spin very fast. Over a thousand R.P.M will do. Choppers can be spun fast by hand- a mechanical siren, or by an electric motor- electromechanical siren.
To aid with the work principle of a chopper/stator, here is a picture so you can get a basic understanding. The picture on the left is of the impeller/stator version; the picture on the right is of the disk method.

The way that an electronic siren works is by speaker manipulation; you simply get your sound through speakers and amplifiers. You can achieve more signals with a speaker than you can with a mechanical siren. The reasons are obvious because all a mechanical type can do is make a tone that is either smooth, or warbling (going up and down.) And a speaker siren can do voice signals; you can bet a mechanical siren cannot come close to that!

Here is also some information regarding both mechanical and electronic sirens: they can either be dual-tone or single-tone. This means that there can be one frequency range of sound coming out of them (single-tone) or two frequency ranges (dual-tone.) For electronic sirens this is only a matter of speaker manipulation; but for mechanical sirens it means having two rows of slots; one row having more slots than the other.

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If any of this seems unclear to you, or you have more questions, please ask me to revise something or give you more information.