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Use AirPlay to stream audio - Apple Support
https://support.apple.com/en-us/HT202809#:~:text=To%20stream%20audio%20from%20your%20Mac%20to%20your,speaker%20that%20you%20want%20to%20stream%20audio%20to.
MacBook to TV but no sound - Apple Community
https://discussions.apple.com/thread/1892077
I would assume that Apple TV would sync TV shows bought via iTunes. As you probably know, ALL syncing from iTunes to Apple TV is a one way street (only TO Apple TV). As to your sound problem, I think I bought my 3.5 audio jack (6 footer) that splits into 2 RCA plugs from Radio Shack for about $5 or so.
How to connect a MacBook to a TV | TechRadar
https://www.techradar.com/how-to/how-to-connect-a-macbook-to-a-tv
If you want your television also to play audio from your Mac, choose the Apple menu, then select System Preferences > Sound. Click 'Output' and …
Connect Macbook Air to TV with HDMI and ThunderBolt …
https://www.youtube.com/watch?v=BjdU_EZIhIU
Connect the new Macbook Air to your TV and enable the sound to come from your TV's speakers.ThunderBolt to HDMI Adapter: http://www.amazon.com/gp/product/B00...
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