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OP, rule out a few things that you can. Unplug it and plug it into another outlet at your home... even try a FEW. This will rule out outlet issues. If you live in an old home, perhaps take it to work or to a newer one and plug in to see if the sound is the same (again, just to test home electrical).

As offered above, plug into a surge suppressor or better- a battery backup UPC- and listen anew. Does that address it?

Lastly, if you can try such things and none of them work, can you take the whole thing into an Apple Store and let them hear the sound? I once had a power supply for a MB well past the guarantee window that started making a buzz sound and an Apple Store replaced it as soon as I demonstrated it for them. Let their ears confirm "normal" vs. not.
 
Is this something one should worry about? Im on the fence buying a M4 Base model, but if this is a common problem I better wait. Not all shops offer the best return politics and issues like these sometimes can be hard to get return or replacement for :X
No, this is not something you should worry about. I’ve had buzzing sounds when using Mac laptops with ungrounded power cords and it goes away when you use a 3-prong cord. But it doesn’t cause electric shock or difficulty using the computer, it’s just a ground hum and there are many ways to ground your power cords correctly.
 
Great, Does seem at least here in Denmark, that it's only supplied with a 2 pin power cord. Thought it had to be 3 pin to be grounded though. But yeah, I guess the buzzing is not a common problem
 
While the discussion seems lively and entertaining about grounding, it is not useful for OP. Minis should not buzz when powered and especially not when unpowered. I do not remember any one of my Macs doing so and surely my Mini M4 is not doing it - it is in living room and would drive my family nuts.
What is happening is that internal power source is buzzing and that is always powered, even when mini is OFF. Used to be buzzing was from loose coils of transformers, but I would be surprised if there still was transformer in this device. But other things loose enough can resonate at 60Hz (Eu) or 50Hz (US...). Grounding will not help - and it is not even possible to do so without adding grounding connection to the box.
This is very likely out of specs and device should be evaluated by Apple and most likely replaced. While likely non-destructive it is surely distracting and shoudl not be acceptable for user.
 
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