I installed 2 smart switches. They are wired back to the panel with an existing 3 conductor 14 (two hots one shared neutral, as per my previous question. The switches buzz slightly, apparently a common thing. But when both light switches are on the breakers in the panel buzz. A slight hardly noticeable, but I hear it. Is this an issue!
I can't know for sure if this is the issue because I'm not there, but I personally have experienced buzzing from a panel caused by corrosion on the bus bars that feed the breakers to the point that they destroy themselves at the back side. I used a plastic and rubberized handled, small brass wire brush to scrub them clean and replaced the damaged breakers and haven't had a problem since.
I don't recommend you remove the breakers and certainly don't touch the bus bars at the back with ANYTHING unless you know what you're doing! Electricity kills. A licensed electrician would probably replace the panel in my mentioned case in particular, but I'm not made of money, so I did it the cheap-arse way.
The buzzing inside the "smart switch" on the other hand is likely coming from the internal relay's coil. The coil is much like a speaker coil, and plays the note that's being sent into it: 60Hz sinewave. This coil is what magnetically pulls the switch contacts together to allow current to flow to your device. There's also a power supply inside to drive the microcontroller unit inside that might be the cause.