Nalates, thanks. All excellent suggestions. Yes, it's the Linden viewer - a version from late 2015, as I'm on Windows XP Pro. It works fine, though.
After a lot of reading around, it turns out this beep is only indirectly connected with Second Life. It is, in fact, a processor temperature warning beep. By the gods is it annoying - and it's meant to be! One of my 4 processors (quad core) was overheating as a result of the demands placed on it by Second Life. (The graphics card was working well within its limits, so overheating wasn't even on my list of suspects.)
So this was a heads-up that I needed to clean my cooling systems, which I have now done. Happy to report that all is well, at least for now. Eventually the machine will need a professional clean.
I appreciate your help; cheers.