My computer is making a funny noise

I have noticed it only recently, a kind of loud hum. It's not continuous but starts up periodically and then stops again. I've traced it to the computer itself. The noise is made by the case, which is vibrating, but obviously it must be picking that up from something inside. If I put a fingertip on the case, the noise stops but I can feel the vibration.

This happens when the machine is idling, so I don't think it's likely to be disk noise. It could be the cpu fan, I suppose, but why would that be so active when the cpu isn't doing much? There is no internal power supply, so no fan there. The power cable has a built-in transformer, like a laptop charger.