Electronics Repair Questions? Ask an Electronics Technician
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Sorry to hear you’re having trouble.
Yes, they can fail, and do so quite often in fact.
Most of those are also a wifi router too, and those radio transceiver components can make noise.
Unplug the power to the 2wire box for a minute and see what happens (power needs to drain out for a minute or 2 after before judging the sound level). It won't hurt anything, though you'll lose internet and possibly phone/cable for a few minutes, but it will come right back when you plug it back in.
If that turns out to be the source of the interference, you can contact ATT and ask them to replace it for you.
Note: You want to actually unplug the wall adapter from the power outlet, not just to unplug the cord from the back of the router. It is actually more likely that the power adapter/brick is faulty than the router, but you can test both ways to find out for sure.