Here's how you can disable the beep sound of Facebook notifications.
1. Click the gear icon in the upper right corner of the Facebook interface.
2. Go to Account Settings.
3. Go to Notifications.
4. Uncheck the "play a sound" option.
5. Click the Save Changes button.
For more, see the original article at the link below.
How to Disable Facebook’s Beeping Sound Notification | How To Geek