the audible noise of an LCD-TFT monitor is coming from the "back light inverter". This inverter generates the power to drive the lamps of the monitor. To reduce the brightness of the lamps the power flowing to the lamps must be reduced. This is usually done by "pulse width modulation" (=PWM). Simply speaking, the lamp is turned on and off very fast. Making the off time longer and longer makes the lamps darker and darker, the brightness is reduced. If the frequency of the on and off period is high enough you cant see the switching of the lamp.
Unfortunately, the frequency at which this takes place is usually in the range of some 100Hz. The result is some "feeping" noise you can hear.
The noise is dependent on the brightness and is usually best heard at low brightness levels.
There are backlight inverter which don't use PWM. This is then called analog dimming. These inverter are noise free. The problem is that the dimming range of analog dimming is smaller than PWM dimming. This is why you normally find PWM dimming in monitors.
Unfortunatly, the way how the dimming is done is not listed in the monitor specs. So the only way to find out is to open the monitor and to look at the backlight inverter.
Of course this is impossible if you buy a new one.
I'm sure all monitor manufacturers are aware of this but most of them just don't care. The primary reason for this is that they say they have no complaints about audible noise.
The only way to improve this situation is to give the monitor back if you find this noise annoying. If more and more customers complain about this it will be changed.
From a technical point of view the noise can be avoided if this is required.
If you want to know more about tis technical stuff look at the specs of a typical backlight controller like the O2Micro OZ965
http://www.o2micro.com/products/OZ965.pdf