The radio/Wi-Fi should be left ‘on’ on the Arc, even if you have it connected by an Ethernet cable. It creates its own Wi-Fi signal that the Sub, and surround speakers to connect to. 

In general, you really should never turn off the Wi-Fi on any Sonos speaker, unless dealing with very specific issues. 

Thanks for the update, just found it a bit confusing, so at least when it’s connected ethernet, the wifi part only applies to the sub connecting to it. Appreciate your help Bruce!

Happy to help. Agreed, Sonos is not very explicit about how their sound bars create their own radio network that bonded devices connect to, so it’s easy to think things are either going back to the router via standard WiFi or cable. Exacerbated by the fact that it still uses your router’s DHCP table to assign IP addresses. Since, at least in my perception, Sonos is trying to be plug and play for people like my parents, they don’t expose some of the more potentially confusing aspects. But if you use them as intended, they generally ‘just work’. It’s those of us who like to meddle with non-standard environments that end up paying the price ;)