DIAGNOSIS: That's likely coil whine from the internal power supply or components, and it's a common, mostly harmless annoyance with many monitors and electronics. It doesn't mean the monitor is failing.
FIX: First, identify when it happens. If it only buzzes when displaying a very bright, static image (like a white browser page), that's typical. Try slightly lowering the monitor's brightness from the OSD. Often, the whine is most audible at specific brightness levels, like 80-100%. Finding a slightly lower brightness that eliminates the noise is the easiest fix.
IF THAT DIDN'T WORK: The sound could be related to a specific refresh rate. If you're running at 120Hz, try dropping to 60Hz via your computer's display settings to see if the pitch or volume of the buzz changes. Also, ensure your room's ambient noise is low when checking—sometimes you notice it more at night and it's actually been there all along.
HEADS UP: If the buzz is a loud, erratic clicking or popping, that's a different issue and could indicate a failing component. A consistent, high-pitched hum or buzz is almost always just annoying coil whine. Dell might consider it within normal operation, so a warranty claim for just the noise can be tricky.