I received my U2713H today (rev A06), and have exactly the same problem.
(Please visit the site to view this video)
It occurs with the provided DP/miniDP as well as with the provided DVI-Cable. Nothing else is connected to the monitor (except power of course). One of the best patterns to prove the effect is to open a notepad and fill the whole screen with "#". This is the loudest effect I could reproduce. So it seems to have something to do with lines and contrast. Now comes the best: I even can change the pitch of the noise! Depending on the zoom size (I'm using Notepad++), I can produce 18 remarkingly different tones! One more annoying than the other. I already thought of making some kind of music out of it. But seriously folks. This is more than annoying. The sound differs if the content of the screen changes as well as if the resolution changes. If the image is flipped 180° I have the same noise, whereas in 90° pivot-mode I don't (which is quite strange, since the "#" is more or less symmetric - so I would have assumed that it produces the noise in pivot-mode as well, but it doesn't. It has nothing to do with brightness setting of the monitor. But if I decrease contrast below 50, it goes slightly better - below 15 remarkably and below 5 (turning almost black) significantly. What can I do besides returning the monitor? I really like it (although I really hate the touch "buttons"), but this noise is really a show stopper. I very often research on Wikipedia, work with spread sheets or edit documents and with all of it, sooner or later I will trigger this annoying noise. With my low-noise computer, it is really more than present. So please, please tell me what I can do besides going back to the shop and buy a Fujitsu.
Thanks
DaVo2k