Hey Wash-Basin,
It appears that you're having a problem with Safari on your MacBook Air. When you play a video on the YouTube site, you only see the video but audio doesn't play. Good job in checking the video and tab weren't muted, and we're glad to provide assistance.
If Safari on Mac doesn't open a webpage or isn’t working as expected - Apple Support -- Even though the steps in this article pertain exactly to your issue, they may help.
If they didn't, we'd like to isolate the issue a bit. Please try the steps below:
How to use safe mode on your Mac - Apple Support -- Restart your Mac in safe mode and see if you get audio with YouTube videos. Whether or not it works as expected, restart your Mac normally to exit safe mode. We also want you to be aware that restarting in safe mode takes a bit longer:
Safe mode prevents your Mac from loading certain software as it starts up, including login items, system extensions not required by macOS, and fonts not installed by macOS. It also does a basic check of your startup disk, similar to using First Aid in Disk Utility. And it deletes some system caches, including font caches and the kernel cache, which are automatically created again as needed.
If the issue didn't happen while in safe mode, test again after a normal restart.
Set up users, guests, and groups on Mac - Apple Support -- If you heard no audio in safe mode or after restarting your Mac, create a new Administrator account. Once the account has been created, log out of yours and into the new one and test.
Please let us know the results when you're able.
All the best.