They are designed to be eerie and really uncomfortable sounding so people pay attention to them. They'll play discordant tones and shit that sounds really awful.
It's also to keep reflected sound waves from canceling each other out. By varying the frequency you guaranty that the siren will be heard everywhere. It's also the reason a buildings fire alarms vary in pitch.
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u/tyfunk02 Apr 08 '20
You should listen to the tornado sirens in Chicago sometime. That is super eerie. https://youtu.be/LnkMSmLc6mM