Welcome Tigerry13,
Thank you for using Apple Support Communities. Based on your post, you can't get sound to work when connecting your MacBook Air to the TV with your Insignia HDMI adapter. We'll do our best to assist with this.
You've done some great isolation, nice work! If the issue only occurs with your MacBook Air and this particular HDMI adapter, then we'd recommend to restart your Mac and test it out again: Shut down or restart your Mac
If that doesn't solve it, what are you trying to play on the TV through the Mac? Are you streaming this content? Does this only happen with a specific song or video? Does it occur within a specific Mac app?
Hoping to hear back, take care.