Greetings. Running OS X 10.9.5 here and a MacBook Pro.
I've had this problem for a long time and its been an annoyance. I finally decided to delve into it a bit. Some of the suggestions here relating this problem to Bluetooth audio got me thinking.
I have had both a pair of Bluetooth headphones and Bluetooth speakers paired with this computer at some point, but haven't used them in a long time and I've typically have had Bluetooth turned off. In fact, I suspect the problem dates back to about the last time the headphones were actively paired with my MacBook Pro.
This is seemed to fix the problem for me: I turned Bluetooth on just so that I could remove the speakers and headphones from the list of paired devices in the Bluetooth control panel. Then I turned Bluetooth off again. Walla, sending and receiving emails now plays the sounds properly.
I hope this helps someone else.
Wouldn't it be nice if Apple didn't leave users to fend for themselves with obscure problems like this, ones spanning years worth of discussions and several operating system versions? Surely someone at Apple knows about this problem, and surely Apple could have someone scour these discussions to provide helpful advice. Oh...I forgot. It's Apple. Don't want to say anything. Lawyers, corporate image, and all that. And, maybe they can't afford to pay someone to do that anyway. Poor, poor, Apple!