This sound emanates from the backlight inverter and depends on the selected brightness value, but also on the vertical frequency.
Failure or not? This is something one can argue about and manufacturers react very differently to claims. Some exchange the monitor no questions asked, other refuse to repair since the sounds are within the specified range.
Next to the settings of vertical frequency and brightness, how good you can hear these sounds also depends on the acoustical shielding of the monitor, or in other words, how large the ventilation slots in the casing are.
The technical background is as follows:
The backlight inverter is the culprit here. It serves as power supply for the lamps. It generates the high frequency alternating voltage required for running the lamps. The frequency of this alternating voltage is way above the range of human audibility. But it is also used for changing the lamps' brightness and this works as follows: The brightness is changed by a so called pulse width modulation, which means that the lamps are rapidly turned on and off at a varying ratio of turn-on time and turn-off time. The longer the On time is compared to the Off time, the brighter it gets. The frequency used for this modulation lies within the human range of audibility however, namely at around 100 to 400 Hz. And that is exactly the problem.
This periodic "turning on and off" of the lamps causes a corresponding fluctuation of current, particularly in the transformer of the backlight inverter. This results in a mechanical resonation in the transformer which then, in turn, becomes audible. This effect corresponds to that of 50 Hz power transformers which are well known for their buzzing sound, too. These are usually encapsulated in order to reduce the mechanical resonation of the coil.
Unfortunately, all backlights inverter work according to this principle. How much one will hear the mechanical resonations depends on the design of the inverter and on how tightly the casing is sealed, of course.