People are being more disappointed with Google chrome beta v4.0.223.11, in my opinion it must be because of their auto download without notification feature, that downloads files before you can notice. Google chrome notifies when the site is trying to download multiple files, and if you want it to stop the files from downloading you can click on yes, it stops to download the file but you wont get the pop sound notification anymore.
This problem might also be solved if You install the flashblock extension which, automatically blocks flash content on webpages and then add www.facebook.com to its white list. However, people are complaining that this extension slows down page loading and gives frequent "aw snap" errors. The problem is caused by .mp3 file not .flv so i don't think there's any thing to do with flash on this problem.
Analyzing all the cases there seems to be no other proper solution than to go to the bottom right of facebook, where the chat is and Uncheck play sounds for new messages. You won't get notifications but you don't have to download pop.mp3 to your hard drive.