I'm having the same problem intermittently. I've found that if I change my output device to my speakers and back to my headphones then try launching Arma again, it'll fix it (although sometimes I have to do this multiple times).

Here's the relevant part of the .rpt (I can post the full RPT if necessary):

11:55:55 Sound engine not initialized properly - dummy sound implementation used, NO SOUND !!!
11:55:55 InitSound ...
11:55:55 InitSound - complete