Is this ringing sound similar to static or an actual sound?
Are you sure that the sound is coming from your sound card and not from some other component inside your system (motherboard alarm, hard drive, etc)?
My first thought is that your system is overheating, and an alarm is going off to tell you about the problem. Can you check your temperatures to make sure that you are not overheating?
If it looks like the sound is coming from your sound card, and it is a type of static sound rather than a soundclip, you might try to upgrade your drivers and see if that helps.
Another idea I have is starting up in Safe Mode to see if the sound occurs in Safe Mode as well. If it doesn't you might have a program that is either creating that sound or is interfering with the sound card somehow.