The game does not use the default audio playback device (in my case, it’s my onboard Realtek HD audio).
Instead it uses the 1st audio playback device that is not disabled.
In my case this was the unconnected “AMD HDMI Output” device (which is provided by the graphics card for piping audio through an HDMI connection to an HDTV).
The work-around is simple enough, just disable any unconnected audio output devices and Brink will not attempt to use them.
However this is far from ideal, as all applications should use whatever audio output device Windows reports as being the default device, not arbitrarily pick one that may or may not be the default device.
If you are effected by this bug, you will hear absolutely no sound at all in the intro videos, the menus, or in-game.
FYI, my specs:
Dell Studio XPS 7100:
Phenom II X6 1055T,
8GB DDR3,
Radeon HD 5870,
Win 7 x64.