I've had this problem for several years and it was driving me absolutely insane. I would get the random tri-tone sound at different times throughout the day despite the fact that there was no notification on screen. I think I finally found a way to fix it and it was easy!
First, I would recommend closing all open apps. Then do a "soft reboot" by following the steps below:
Performing a soft reset is pretty simple
- Just press and hold both the Sleep/Wake and Home buttons simultaneously for at least 10 seconds, until you see the Apple logo. You can let go of both buttons after the Apple logo appears.
- Your phone will go through the usual process of starting up.
- You’ll be back in your home screen.
After this, I never got another randome tri-tone sound. If it does happen, just do another soft reboot. Just had to share since nothing I tried ever fixed it. GL!