Q: No sound through tv from hdmi - Macbook Air

Check your "sound output" setting > OS X Yosemite: Adjust your computer’s sound output settings - ÇÇÇ

If this persists after you go through the article, let us know.

Here is some info:

About Mini DisplayPort to HDMI adapters - Apple Support

Is the mini display port what you used? Or the Thunderbolt? I had an older MBP and had to use the regular audio cables  (red & white) in addition to the mini display port adapter.

As I'm not sure about your model and the support of transmitting sound, have you tried audio cables (red & white RCA) in addition to the regular cable?

Also consider the possibility of a faulty HDMI cable - it happens with brand new stuff more often than folks think. It seems that until you prove that sound plays from RCA cables, then try a different HDMI cable (consider a different brand as well) you will never know what's what.