Thanks a lot, hilalpro! :)
I didn't have to do anything - just closed all programms, installed dfx audio enhancer and I was fine.
No TeamSpeak-sounds in the stream.
Next question: Is there an alternative to dfx audio enhancer ? It works fine, but I don't want to pay for it and it's a bit anoying to click on the "no - I really don't want to buy the pro version now"-button every 5 minutes.