Howdy, Virginia native who lives near these sirens. AFAIK, they were indeed installed after 9/11 - around 2004. Their usage is unknown.
The Pentagon simply installed the siren to put it in short.
As for the WAVES siren, it was a pilot system ran by Arlington and Alexandria County's. Lucky for me, someone from then was able to record the sirens on their monthly tests (or weekly - it's been so long since I've went back to this system). Very similar to the Pentagon system - all came after 9/11.
If you'd like a rundown on it's history, it was drafted in 2004 and called for action around then. Funds were raised - over 400K for the installation of 10 sirens in Arlington and 3 in Alexandria. It ended with only 6 sirens in total coming about with all of them being removed around 2017ish with the replacement of traffic light poles they were once on. The only ones that remain are at parks on lightpoles and simply forgotten about. The last instance of these sirens ever being used was 2014 from what I was able to gather.
Here's the video :
https://www.youtube.com/watch?v=8kKoPGX4Hj0
Amazing how clear the voice are on these sirens.