Storytime. I have a coworker in the office next to me who gets super duper anxious when the heat drops on deadline day. Like the sky is falling but for reals, and has to talk through the entire thought process on it with anxious inflection. We're talking non-stop, can hear it through the walls with my door closed and earbuds in. I finally couldn't take it one day, and went to the group manager and said it was routinely effecting my tasks. I was told I could openly discuss this distraction with the source in a professional manner, as nothing should ever prevent someone from performing their job efficiently. So I did, in a concise yet cordial manner. ...A little different version than your distraction, but I would tell them their whistling is triggering your rage and that they wouldn't like it if you got mad. jklolsHow do you tell a coworker to nicely stop with the damn humming and whistling, this is an office and not a middle school cafeteria?
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No I would simply ask them "Excuse me, I'm really trying to focus on <Insert task here> and the songs you whistle tend to distract me. If you could please hum them in your head, I can stay productive and get <Insert task here> to our <Insert mutual manager here> in the timeframe they are expecting."