Does the TV have any sort of audio output?

You can connect a Sonos Beam or Sonos Arc to your TV if it is equipped with an digital optical/TOSLINK output using the HDMI to optical adapter that comes with these two soundbars.

Thanks!  Don’t see my previous response anymore, so here’s another picture of the outputs on the back of my TV. Sorry about the dust  

It looks like you already have something connected to your TV’s optical output.

Is this the one? sorry for being a noob.  

Oh! Looks like it’s plugged into the receiver that no longer functions, hence my need for a sound bar. 

Yes, that’s the output that you would need to connect to the adapter that gets plugged in to the Sonos Soundbar. I’d be tempted to try to use that same cable, but cable looks kind of old, so it could be ‘broken’, optical cables can be slightly more sensitive than ‘regular’ cables. 

You should be able to connect one of the SONOS sound bars here. It would pay to examine the connecter type in order to make sure that you don’t need some sort of adapter. Your connector looks like it might be the round style -- which is not compatible with what is packed in the SONOS box. It’s not a big deal, but it could dampen your spirits on day one.

Thank you so much! 

@gangofcentaurs
It’s not clear from the photo, but it looks to me like your TV has a coax optical out port, if so, you will need another converter to switch that to Optical Toslink.. Something like this (just a quick example I found on Amazon)…

https://www.amazon.co.uk/Cable-Mountain-Digital-Coaxial-Converter/dp/B001U7GW68

Then (if relevant) use the Optical to HDMI adapter (supplied with Beam/Arc) and the HDMI cable connected to your chosen Sonos HT product. All being well that may work for you.

Also, if you intend on getting a Sonos Arc, note that an Atmos signal can not be carried across optical, the best you may receive, depending on the electronics in the TV, would be Dolby Digital.

Thanks! I saw that, and opted for a beam. 

There are available adapters, if as buzz suspects, the optical cable has the ‘wrong’ kind of connection. Just search on Amazon, although there is no requirement to purchase there, it’s just a good place to see options, as desired.