Given that everything I have is just weeks old and all 100% Apple, you have to wonder how Apple screwed this up. Do they even test things before forcing them on us?
My Apple Macbook Air, connected to an Apple Airport Extreme router, using Apple Safari to stream video to an AppleTV -- all purchased in December 2013 by the way -- worked fine until I applied the latest AppleTV update. Suddenly video could go through the AppleTV, but the audio only came from my MacBook Air.
Of course I tried again and again to switch the audio output to AppleTV via System Preferences -> Sound -> Output, but it kept snapping back to the internal speakers.
Finally, after looking over every possible setting on the AppleTV and my Macbook Air...
1. I unplugged the power cord of the AppleTV
2. Unplugged the HDMI cable from the AppleTV
3. Unplugged the power cord to the Apple Airport Extreme wifi router
4. Waited 30 seconds
5. Plugged the power cord back into the Apple Airport Extreme wifi router
6. Plugged the power cord back into the AppleTV
7. Plugged the HDMI cable back into the AppleTV
And like magic audio still did NOT work.
Because I was using Firefox, I tried an experiement: I pasted the URL from Firefox into Safair and TADA! Suddenly audio and video was coming out of the AppleTV.
Curious, I then the URL into Chrome... no audio again.
So for me, the fix after the AppleTV update requried pulling the power cord of both the router and the AppleTV, and using Safari and not Firefox or Chrome.
Hope this helps someone.