Sound alerts on FB messenger

Of course, make sure you go through the first set of troubleshooting steps. It may sound silly, but always check:

-That your phone is not on "Silent" or any form of "Do Not Disturb" Mode

-Go to Settings<Sounds & Haptics and make sure "Ringers And Alerts" is actually turned up.

-Go to Settings<Notifications<Messenger and make sure everything is set up correctly there

If the above is okay or does not solve the problem, try re-installing the app and restarting your iPhone.

Remember that while you're in the Messenger app, sometimes you will receive no sounds notifications.

Here's an article that might have more steps and tips to follow.
https://appletoolbox.com/2013/09/facebook-push-notifications-working-fix/

I would also advise trying to mess around with the Facebook settings on your phone as well, as I have heard that has fixed similar problems as well.