I think you have a ground loop. Either your house's wiring is not properly grounded to the main ground, or you simply do not have a ground wire in your outlet. That sound clip is an octave of 60Hz which is what the AC power coming from the wall is. The rear audio outputs are near all USB and so they are more prone to interference that you are hearing. I bet if you move your mouse you will actually be able to hear the sound of the static change.
Go on Amazon and buy a ground loop isolator. Put it between your headset cable and the motherboard output. They able to nearly fully eliminate the static noise you're hearing. If it doesn't solve your problem, you might have a different issue. They're like 10 bucks or even cheaper. https://www.amazon.com/Mpow-Ground-Isolator-Stereo-System/dp/B019393MV2/ref=mp_s_a_1_3?ie=UTF8&qid=1549285675&sr=8-3&pi=AC_SX236_SY340_FMwebp_QL65&keywords=ground+loop+isolators&dpPl=1&dpID=41muoMylGtL&ref=plSrch
You might need two (one for headphones, one for microphone) since yours terminates to separate plugs (do a quick mic recording to see if it's in your mic recording too), but just buy one to see if it solves the issue.
Good luck.