... If you follow the thread I posted, there are many with this problem. They are told to do resets and other things but nobody seems to have found "it" although some folks seem to have gotten rid of the beep (at least as of the time of their posting).
I don't have the issue, so I have no experience in this. I just have read a lot of messages from some very frustrated people and hope there is a well published answer soon.
It's difficult, since "beeping during a call" can be caused by a number of things, and in this case may very well be a software issue that can be fixed with an update (the well-published answer you are looking for!). Those folks that seem to have gotten rid of it probably found whatever setting or app was causing it to beep and changed it (and it could be any of several notification "beeps").
The only way to figure it out is to systematically go through all the settings that COULD beep at you and adjust the settings; it will be a tedious process. And based on the volume and consistency of the complaints, it may be something inherent in the phone (software). Really hard to say....
Yes, I'm sure that sometimes it is a software issue where it can be uninstalled or tweaked to solve the problems. But some other of the posts I've read on different forums speak of resetting (not rebooting) their phone and with no notifications on or other apps yet installed, still having the problem. They've taken it to VZ dealers who also have confirmed this.
If you have read the linked thread you know that it's not a DROID RAZR problem. Other phones are reporting it, but they do have Verizon in common. So calling and logging an issue might help them gather enough data to figure it out.