They're Not Tornado Sirens
There is a great deal of confusion surrounding outdoor warning sirens and what they mean. So, allow me to explain what the sirens are really used for and how you should react if you ever hear them.
Fact One: The sirens are used for all hazards (not just weather).
The original purpose of the outdoor warning system was to alert people about a potential nuclear strike or an enemy invasion of some kind. Some of the oldest sirens date back to World War II when they were originally built, but some communities have either modernized the sirens or built their own siren network. Many modern sirens are capable of generating multiple tones (frequencies), and some are even capable of broadcasting a verbal alert. However, even the louder and more powerful modern sirens cannot reach everybody. In fact, they're primarily intended to warn people who are outdoors. The sirens are not effective at reaching people indoors (unless you happen to be very close to one), and they're even less effective at waking people up if they're asleep.
Don't believe it? Well, here's an excerpt from the United States Department of Homeland Security:
"Outdoor warning sirens generate sound through mechanical, electromechincal, or electronic means, and can produce audible signals ranging from tones of varying pitch, frequency, and duration to pre-recorded and live-voice messages. These systems are used by public safety agencies to alert people about natural and man-made hazards."
Source: www.dhs.gov/publication/outdoor-warning-sirens
When you look at when these sirens have been activated, you'll find that weather hazards are so much more common than man-made hazards. After all, how many times has the United States been hit by a nuclear missile? 0. How many tornado warnings get issued per year in the United States? Several thousand. This is the reason why these sirens have colloquially been christened "tornado sirens", even though they are used for more than hazardous weather.
If you still doubt the feasibility of these sirens to reach everybody (indoors and outdoors), do a little experiment the next time your city's sirens are tested. Compare the volume of the sirens when you're indoors to when you're outdoors. When you're inside, ask yourself "would this be loud enough to wake me up in the middle of the night?" Unless you happen to live very close to an outdoor siren, then the answer to this question is "no". If you've never heard a siren test before, then the sirens are either impossible to hear when you're indoors or your municipality doesn't even have sirens to sound (not every town and city has outdoor sirens).
Fact Two: Sirens are controlled by city managers, making siren policy inconsistent.
Since the outdoor sirens are commonly called "tornado sirens", there's also a misconception that the National Weather Service controls the sirens. They don't. The sirens are directly controlled by city emergency management agencies or a coalition of first responders (in the case of rural towns).
Granted, the National Weather Service can issue alerts that prompt the activation of sirens, but they themselves cannot activate the sirens. Emergency management personnel (not affiliated with the National Weather Service) make the final decision. Some cities will automatically trigger their sirens if a specific alert is issued (e.g. a tornado warning), but an operator can always shut them off even if the alert is still in effect.
Since each city and town is different, their siren policies and procedures will also be different. Some cities will have the sirens running for the duration of the tornado warning. Some cities will not activate the sirens until the storm gets close. Some cities may not activate the sirens at all, because they may have someone telling them the tornado will not occur within city limits.
Some cities like Arlington, Texas will activate sirens for a severe thunderstorm warning if damaging straight-line wind gusts and/or dangerous hail is expected. For a city like Arlington, this makes sense, because there are several highly vulnerable outdoor venues with limited shelter options (e.g. Six Flags). Some cities like Tulsa, Oklahoma will activate sirens if major flooding is occurring. Again, this makes sense, because Tulsa sits in a valley, which increases the risk for dangerous flooding and deadly landslides. To make things even more interesting, some cities will only activate siren towers that are within a warning polygon and keep the other sirens off.
The city-to-city differences in policy are also evident in another way. Sirens are tested on a regular basis, but that "regular basis" is different in different cities. Some cities test monthly. Some test weekly. Some test on Saturdays. Some test on a Wednesday. Some test at noon. Some test at 1 PM.
In the interest of proper preparation, I strongly recommend that you research what your municipality's siren policy is.
Fact Three: Sirens cannot perfectly encapsulate a warning polygon.
Whenever a tornado warning, severe thunderstorm warning, or flash flood warning is issued, a polygon is drawn to indicate what specific area is at greatest risk. By the definition of a polygon, there is a series of straight lines that connect to form a complete shape. Do sirens broadcast their signals in these patterns? No. The broadcasts are omnidirectional, which means the sound travels in all directions to form a circle of sorts. A circle, being round, cannot possibly match the shape of a polygon, even if there are many sirens and circles.
This means that if you're near the edge of the polygon, you may either get unnecessarily warned or you may not get any warning at all. Remember the discussion about how some cities only sound sirens if the towers are within a polygon? Turns out, it is possible for your house to be within a polygon, but the nearest siren tower is not, meaning it will be silent. The reverse could also hold true. Your house could be outside of a polygon, but the nearest siren could be in the polygon, meaning it will be blaring.
Notice that another complication has been ignored thus far: everyone's ears hear differently. Sirens may audible to you if you have sensitive hearing, but may be inaudible to your neighbor. This is a real problem for people who have hearing impairments.
Fact Four: Some institutions use their own outdoor warning systems that are independent of the main system.
If you live near a school that has outdoor athletic facilities, there's a good chance that you've heard an alert tone that is different than the normal outdoor warning system. Usually, this is an automated lightning sensor sounding its alert tone. The outdoor warning system I've been discussing this whole time will probably never be sounded for lightning. After all, imagine hearing the sirens every time there's a thunderstorm (if thunderstorms are rare where you live, this might actually happen).
Many schools and gyms use these lightning sensors as an automated alert of sorts, telling people outside that lightning is approaching and they need to seek shelter. Sometimes, these instruments perform reasonably well. However, sometimes these sensors perform terribly. They usually don't sound false alarms, but they have been known to mistakenly sound an "all clear" signal. Plus, many of these automated systems will only sound an alert when lightning is first detected. If you're inside while the alert is sounded and then walk outside after the tone has ended, you might be unwittingly putting yourself at risk of being struck by lightning. That said, these systems usually have a blinking light if the lightning risk is active, but you have to know where the system is mounted in order to see that light.
In some small towns, an outdoor warning system is sometimes used to rally volunteer firefighters since rural areas don't have a centralized fire department. Thing is, the same sirens used to rally the fire brigade can be the same sirens you would hear if a hazardous weather alert was issued.
Conclusions
Solely relying on the outdoor warning system is often a risky gamble. You're better off receiving alerts from a smartphone app or a NOAA Weather Radio. By smartphone app, I mean an app specifically designed to alert you when a watch or warning includes your specific location (one good use for a GPS chip). General weather apps may not do this. If you don't own a smartphone or don't wish to pay for an app, you can enable Wireless Emergency Alerts (WEAs), which are free and also pretty effective. More discussion of this in No, There Is Not An App For That.
If you ever hear the sirens and the sirens are not being tested, it means you're in danger if you're outdoors. The proper course of action would be to seek shelter in the nearest safe and well-built structure and try to find out why the sirens are sounding. Sometimes, the sirens malfunction, but you need to be 100% sure about what's going on before going back outside.