When you run a current through a wire it creates a magnetic field. Flip that current on and off real quick and you'll get a vibrating wire. Coil that wire up real tight to make an inductor and now you've got a thing vibrating at a high frequency and possibly having an audible frequency getting kicked off

Coils vibrate, it's just what they do. Normally they're running at hundreds of kilohertz to megahertz so it's way beyond audible range but sometimes it makes the core rattle at an audible frequency, but it's hard to fix by winding differently

Common solutions are a big dollop of hot glue(yeah, just normal hot glue, it's cheap) or dipping the coil/transformer in varnish (clear nail polish). Both solutions just bind things together better so they can't move/vibrate as well