The traction motor in my car is virtually silent and was noticeably quieter than the Leaf I test drove beforehand, though I didn't find that car's sound objectionable. The Soul has a very high-pitched inverter that can be heard if the windows are down and you're driving alongside a surface that can reflect sound, however.
The only noise my Soul makes is the brake system doing its thing when it switches from regen to friction. I can hear a little bit of racket from that, particularly creeping along in traffic with the radio off. Otherwise the car is effectively silent.