This doesn't address your question exactly, but it's as close as I can get. Considering it's been over three years since this was posted and there isn't a better solution, this is probably the best we can do. This is, essentially, an expansion on Rowe's solution.
Sorry, but them's the breaks. But what you can do (at least in windows) is individually control the volumes of different running programs. So if instead of visiting different websites on different tabs, you visit them with different applications, you can control the volume by clicking the "speaker" icon on the windows taskbar and then clicking "mixer". For example, visit one website in chrome, and the other in firefox or IE. Rowe suggested installing chrome canary as your second browser, but any browser application will work.
Here's a step-by-step for accessing the mixer in windows 7: