Hi all,
I originally posted Nov. 24. I just wanted to give a quick update - the issue has't come back at all since my post in November. iMessage, for me, had nothing to do with the issue, as I didn't have it on in the first place. It may be the issue for some, but if that isn't working. . .
I did have vibrate with notifications turned on, but I turned it off. This made the issue go away, turning virbrate with notifications back on did not make the issue come back.
I want to be clear about iMessage as well. I had fully set up iMessage when I did the update to iOS 5 the day it came out. A few days later, I turned it off because I didn't like it. Much later, the double tone started. In an attempt to fix the issue, I turned iMessage on and off, and restarted the phone several times - nothing. I also turned iMessage on the other day, after having fixed the issue on my phone. It didn't cause the issue to come back. I haven't found a setting that has caused it to come back yet. So iMessage could be one issue, but it isn't the only issue.
It seems there is a trend in all of these responses, that simply turning on/off different settings within notifications and messages, then doing a reset (holding home & power button until the phone reboots), may fix the issue. It will probably take a lot of trial and error to find what may be causing your issue, and it may never fix the issue on your particular phone, but it's definitely a good starting place.