I'm a youtuber pianist. Sometimes when I record my electric keyboard through audio in of ZOOM H2 mic, I can hear a low buzzing sound. This is really annoying because I have to redo all! Do you know what it can be? The WiFi?
A vacuum cleaner.
True story: a friend of mine used to be an organ tuner. So he was there in a church, doing the final intonation of the registers (that's even after the tuning, making sure that all of a register responds in style and consistently) and all the personnel had been notified of the requirements for absolute silence.
So he is working on this one pipe which has sort of a buzz or howl. Spends about an hour trying to work on it, with the apprentice holding the keys, and him listening and identifying the bad pipe, then taking to work on it, getting out again and so on. Works on that pipe for the better part of an hour before finally the buzz/howl persists for a few seconds even after the key is released. "Oh great, now I have a howler as well." "Master, I don't think that's from the organ."
Turns out that the cleaning woman was vacuuming in the sanctuary. And because of the instructions to keep absolute silence, she only vacuumed when the organ was making noise anyway. Which didn't exactly help.
There was a scene. A bad one. My friend had to apologize for it afterwards.
Getting back to your buzz: my personal bet is more on a switching power supply or a refridgerator. First measure would be recording with batteries in your recorder rather than a power supply. That's pretty easy to try. If it doesn't help, loop at electric devices in the vicinity. Power-saving light bulbs have switching supplies that can, particularly at the end of their life time, cause interference.
An H2 is not all that sensitive, so my bet is on electric interference. With good preamps and large diaphragm condensers I actually had to take off and bury in cushions a wall clock two rooms away so that my "silent" noise floor was indeed silent rather than ticking.
WiFi is unlikely, at least not with regard to radio interference: that's rather weak. Mobile phones, however, are pretty strong in that regard. They don't just need to get through to the next few rooms but half across town. That results in seriously stronger potential for interference.