Same exact problem! After logging in sometimes there will be no sound either through headphones or built in speakers. A restart fixes the problem but its annoying how often I need to do it now.
Yep, I have this too on my 2013 13" MacBook Air 1.3GHz/120GB/8GB. It only started when I installed Mavericks. Under Lion it was fine.
Seems to occur mainly when I try to use an app that uses sound input or output (eg. Skype, Quicktime player, etc.). Sound will then disappear altogether, even though I can use all the volume sliders, etc. without any problem (they all work fine except I get no audio feedback of course). A restart is the only way I can get the sound to work again.
I certainly hope Apple recognise this & fix it in the next update.
I have no idea whether or not this is related but, just in case it is...
I have also found that, on reboot, after I select the user & enter my password inn the login screen, I get the desktop appearing for a few seconds then it drops back to the login screen again. This may happen 2 or 3 times before it manages to stay logged in.
As I said, no idea whether or not this is connected or if it's a separate problem.
TV