Well I'm no techie but it sounds like a capacitor...
Is it from the A4000 or the monitor? There was an article here before
about the A4k's electrolytic capacitors aging. Maybe a more
technically minded person can walk you through isolating the problem.
I've had some weird noises from my Amiga before - sometimes when I
crash my scandoubler will squeak like a mouse (unless it's just the
monitor going funny at the video signal).
Also, I've heard a Quantum Fireball on a PC with bearing trouble and
it sounds like a ping-pong ball going up and down.
I once had a PDA that used only solid state hardware and on a quiet
night you could hear the processors, like a faint hissing noise. This
could just have been the power fluctuation to the speaker though.