Do quiet induction burners exist?

Quieter, yes. Quiet, no.

This was based on my recent research where I tested out 8 different portable induction burners, did a lot of reading, and ultimately decided not to buy one.

Induction burners make noise for two main reasons:

1. They work via a spinning electromagnetic field, which causes both the burner and the vessel to vibrate microscopically, creating a loud hum.
2. They have an internal fan to keep the electronics cool while the burner is on. This is often the louder source of noise.

Higher-end induction burners produce less noise by having a heavier case (reducing vibration), and by having a better cooling fan. However, having tried some of these fairly expensive commercial burners, like a Waring and a Vollrath, I'd say they are quieter but not exactly something you'd use in a room with a sleeping baby.

Built-in burners can reduce noise further simply by having sound insulation built into the cooktop, and many do.