The buzzing normally changes if you change brightness/contrast. It should reduce buzz if brightness is turned up.
I'll make an informed guess here.
I think it's coincidence - you're running on low brightness so there's a buzz.
But I can't ignore the UPS point. I'd bet that the UPS (maybe a cheaper one?), without proper mains synchronisation (50Hz in the UK, 60Hz in N. America) the UPS A/C output is not perfectly sinusoidal which can induce the buzz via the input mains component. I would expect the buzz to disappear if you turn up the power demand via the brightness control, but that depends on the monitor's design.
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Posting Virtuoso
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since Aug 2007