I just got an RX 580, and I've noticed that 9/10 times, when I turn on the monitor while the computer is already on, there is static noise for a whole 2-3 seconds before going to normal. I've done a clean install of the drivers but to no avail. Check it out here:
you may be hearing the caps come on when the monitor sees the pc is on and power up to full on from full off. most newer monitors go from sleep to on now and dont need to be turned off.