Monitor High Pitch Noise

It could be a bad power supply design. Monitor screens are complicated at a low level, and often have some very small power supply elements in one or more locations built in. These are usually very small supplementary elements that create local higher voltages or differential voltages.

I don't recommend taking anything modern apart unless you know what to expect and have the tools. It is super easy to screw up a display when one is disassembled.

Most of the time, what you are hearing is the actual magnetics vibrating from the frequency of the switching operation and load. There is likely a major harmonic of the switching frequency that is falling into the audible range.

One trick, if the monitor has an external power brick and you happen to have another unit around that has a similar rating, you can swap out the power supplies. This might change enough factors related to frequency and capacitance in the circuit to alter the behavior. If the power brick is from another source it is more likely to alter the behavior, although even the same supplier's power supply may alter the behavior. The output capacitors in the circuit generally have a 20% tolerance rating. So even with a power brick of the same frequency and design, simply changing this may have an impact on the undesirable noise. It really depends on to overall topology and design as to how this will impact the issue, but in the off chance that you have a bunch of old power bricks laying around, it is an easy test. The only things that matter are the same or higher watt rating and within ±3 volts for the rated voltage.