All sensible answers amaltman. I was going to suggest that your computer's sending you subliminal messages, but I didn't think you'd appreciate that reply before the others'd said first! Sorry.
Hope you soon sort the problem out.
I'd have suggested opening it up, locating the speaker and cutting the wires to it. But as the beeping may be an indication that something is wrong, go with AC's response first :-)
I'm still reading all the answers. The sound isnt a bing it is a beep and to describe like my grandson did, it was a beep that he didnt have enough breath to finish it.
any help
ok - swap bing for beep ...
is it still beeping? (you say tomato and all that - as long as it's not playing abba it's not realy an issue)
1 long?
did it affect the machine - make it shutdown or pause
back to the keyboard - when a key sticks it beeps - the repeat rate sets how frequently - fast sounds like 1 long beep (bing?) - you move your arm, book - whatever and it stops
the other option is the one everyone has latched on - it's overheating.
laptop or desktop?
(look back or search these pages - you'll find 100s on how to clean the inside of a machine)
What your grand son described could be a short circuit in your speakers, which give an audible sound intermittently with even the slightest vibration....so try moving them,or if built-in,remove 6.3ml plug on rear,then replace. if it is this, don't forget to replace cable.