As rtware923 stated, DVI can't carry audio. However, that's actually irrelevant. If you try the same thing with DisplayPort and HDMI (both of which carry audio), or even HDMI and speakers, you will discover that only one can have sound. As thormejh points out, Windows has a limitation that it can only output sound to one audio device at a time.
There's a hack you can do to have your sound card's mixing hardware pick up the computer's sound, and direct it to a second audio device. But there will be a slight lag in the second audio device's sound (it has to be processed by the sound card's mixer first), which will create an annoying echo effect if your two audio devices are monitors sitting next to each other. Also, I'm not sure if...