How to clear “bell” flag (icon, sound) in Terminal tab

The Terminal tabs in OS X can sometimes trigger a persistent "bell" condition where a bell icon appears in the title tab, and every time I navigate to that tab using cmd-tab, the alert sound occurs, and the bell icon fades away, and then whenever I change tabs again, the alert sound occurs again and the bell icon reappears. Switching screens can also trigger the same pair of alert sounds.

The upshot of all of this is that I can easily enter a condition where I'm hearing spurious alert noises many times per minute; it's irritating. Obviously, I can just close that particular tab, but this causes several problems–I many have long-running processes in the background of that tab, or a specific arrangement (the leftmost tab contains a particular job, for instance.

EDIT: I think I didn't make it clear that I don't want to disable the bell sound; I want it to occur when a bad thing happens. What I don't want is for a given Terminal tab to have a permanent error condition where every change to that tab sounds the bell.

Here's a movie:

https://brinckerhoff.org/tmp/terminal-bell-movie.mov

Unfortunately, these movies don't include the irritating sound–I think Apple doesn't want to make it too easy to capture computer audio–but you can see the bell icon disappearing and reappearing, and imagine the bell occurring for both of these.