Sudden loud continuous bleep on one account when computer is idling

Nobody has touched the computer for a bit - it's asleep; and then suddenly the room is filled with an overpowering long, continuous bleep kind of whistle. It goes on and on steadily and won't go away unless we change the user. It doesn't seem to affect the operation of the computer (a 27" retina iMac) but it's scary when it starts up and loud enough to wake people up upstairs. 😮

Strangely this has also happened, just once, on my 2006 MacBook Pro (still going strong with an internal SSD - and hanging on, hoping for another 17" model some day, yes!); and I had to restart to stop the sound. Only that was more what might be described as a 'parp' - i.e. lower pitched and more saw-tooth wave rather than sine wave.

Any ideas? Are our machines and data safe? And can we stop it from happening? I notice there have been people complaining of such things since around 2008. Surely someone has found a cause and solution by now?