There's one potential solution that I've found which doesn't involve restarting your computer or messing around with C++ installations.

Exit Risk of Rain Then close anything using Flash (ie: web browsers, other games, etc) Restart Risk of Rain normally

For me, this issue manifested when I had some YouTube videos open in Google Chrome then started up Risk of Rain. Closing the specific tabs wasn't enough; I had to close Chrome itself before the sound worked properly.