I'm getting a constant popping noise, too. I've watched my sound sliders in the windows volume mixer. The pop registers as coming from STO.
The pop occurs whether the game is maximized or minimized. I've tried turning down each individual volume slider ingame and seeing if it disappears, and even with all of them down to 0%, the pop still occurs. It doesn't matter where I am ingame; it's not an issue with anomalous ambient sound files. It's EXTREMELY annoying, and I find it highly inappropriate that Cryptic would allow something like this to continue on such a large scale.
I use a Corsair Vengeance 1500 headset. If memory serves, the popping also occurred when I was using my Razer Megalodon. The sound only seems to occur, based on these reports, in high-end headsets and/or headsets with USB plugs.
On an unrelated note, my other high-end gaming equipment has trouble registering keystrokes properly ingame, often hitting more than one ability simultaneously but unintentionally. I'm quite aggravated that high-end gamers get penalized for using high-end equipment in STO. Whether it's keyboards, mice, or headsets, only the average 15$-40$ garbage seems to work properly.
I had/have similar problem , how i fixed it now is by putting the STO volume down in the windows "volume mixer", then turn up the "overall volume" to your liking, it is still there for me, but its just a "zip zip" zound as if you hear a wave file clipping over...
When it was turned up higher in volume mixer, it would pop so loud it was painfull for my ears...
I've seen this issue in a lot of other games before. If you have a surround sound headset, you will have to set your speakers to just 2 speakers. For me at least, that's what has fixed the problem. It doesn't even sound any different for me. Though of course the difference is noticeable in other games.