TV to Beam/Arc/Playbar via HDMI-ARC or s/pdif optical. WiFi has nothing to do with it.

My TV does not have any output jacks

You would need to add a Sonos Soundbar or Amp …and connect either to the TV and play the audio to the soundbar and group it with your Sonos speakers. Note there would be a slight delay to the grouped speakers due to buffering, but you may not notice this is your grouped speakers are located in different physical rooms.

Some Sonos speaker ‘pairs’ can be ‘bonded’ (rather than ‘grouped’) to Sonos soundbars and Amp for HT surround audio, and they will not be limited by the buffer delay and can be used in sync in the same physical room, but note these things may depend on the type of A/V source being played - ideally you would want 5.0/1 surround sound from the TV/Roku rather than PCM stereo audio.

Hope that assists. 

It initially sounds like it maybe too old to support Sonos speakers but you might need to give more details of make/model etc.

TV has no output jacks. I just have the Roku streamer.

TV is a Samsung Model: LN480503F8FXZA

If I have to buy a new TV, Is there one that will play the sound through my wireless Sonos Ikea speakers?

No. TV audio needs a cable of some form.

Wow, not sure how Samsung were allowed to sell this in the USA. The law requires an optical output for ATSC devices, but this has none. You need a new TV.

I can’t find anything online about that TV model, but if it doesn’t have an Optical or eARC audio out option, then I would perhaps forget the Roku connection and perhaps wait until after you’ve upgraded the TV.

The only other thing is if the Roku has a Bluetooth speaker-link you could output it’s audio to the Sonos Roam and group the Roam over WiFi (at the same time) to your Sonos speakers but I cannot vouch for the reliability of such a connection, but mention it in case you wish to perhaps explore the idea.

Could the Sonos app add TV streaming services as a source and route the sound to Sonos speakers, but the video to a TV ?

The App is just a remote for your speakers. It doesn’t do what you’re asking for.

It does connect to streaming music sources. Perhaps a feature could be added so that it can connect to streaming TV services too.

It would have no way to sync audio with the picture, so it would blow chunks.

You’re saying the Sonos developers are not smart enough to figure out how to sync the video and audio signals? I think the Roku developers are able to do it somehow.

And as a result Sonos would sell fewer soundbars and only possibly some extra  speakers? Investing in programming for this does not seem like a good business decision.

LOL well Roku plays the video and the audio, so I would very much hope they would be in sync.

Sonos just plays audio, it has no idea about video.