A high pitched whine is not necessarily an indication that the monitor is dying. There are a number of things that can cause a whiny high-pitched sound. It is almost always due to vibration of a component in the horizontal circuits, most often the flyback transformer or horizontal output transformer. This is why a good wack to the side sometimes temporarily fixes the problem. It will not get better over time only worse. I do not recommend you attempt to fix this yourself, unless you are trained and very comfortable working with extremely high voltages.
A service technician should be able to find the offending component and either replace it, remount it, or add some material which will stop the vibration. It may also stop if you simply run the monitor at a different resolution or refresh rate. If the monitor is under warranty I suggest you send it back for a replacement.
Good Luck