Had one of those for a looong time when I was in middle/high school. My teachers especially loved how it emitted 2 strident beeps at each hour.
And indeed, that was the most efficient watch I ever had.
The frequency at which those beeps are emitted, and the fact that there are, as you put it, precisely "2 strident beeps" makes it impossible to locate by sound alone. I misplaced one of these a decade ago somewhere in the "mess that is my home office" and had been punished with these two, maddening, beeps going off every hour for about nine of those ten years. I'm not sure if it was found by someone else or the battery finally gave in, but it used to drive me crazy.
Let's face it, that's not a problem with the watch per se :)