It doesn't happen to mine but I can see how it could - the liquid crystal is driven with a high-frequency signal whose voltage basically corresponds to the intensity of the pixel, and when images containing repetitive content are displayed, that signal will follow the content of the image; the current that drives the display also follows that signal, and if the signal contains frequencies that happen to excite resonances in the audible range in some components of the hardware, you can hear it.

http://en.wikipedia.org/wiki/Coil_noise

http://www.ukgamingcomputers.co.uk/capacitor-squeal-coil-whi...

http://electronics.stackexchange.com/questions/34806/what-mi...