Since posting my message I have done some additional tests.
I went through all the Windows sounds, and discovered that the beeps I am hearing are the sounds:
Windows Hardware Remove.wav
Windows Hardware Insert.wav
The remove sound happens first, immediately followed by the insert sound. These sounds are identical to the sounds made when you add/remove a USB device, such as plugging in a USB drive, or a USB mouse/keyboard.
I checked and saw that I had a USB drive inserted in a USB slot. I removed the drive, but the sounds continued.
Next, I figured that perhaps my mouse or keyboard (both USB devices) had worked loose in their sockets, and were intermittently disconnecting/connecting. So I unplugged them from their sockets (in the front of the computer), and plugged them into spare USB sockets at the back.
After I did this, for quite a while I got no beeps at all, and I was thinking that perhaps I had solved the problem.
However, about 10 minutes later, I heard another beep like before. It has not been repeated in a while, but it makes me nervous, because it seems to show that the problem was not entirely due to a loose USB socket at the front of the computer.
Any help is appreciated.
EDIT: I forgot to mention it earlier -- I don't have any other USB devices plugged into the computer. The USB drive, the mouse, and the keyboard were the only USB devices. The USB drive has now been removed, and as I mentioned above, the mouse and keyboard have been moved to different USB sockets at the back.