Here is what I did to find a pesky application playing a system file. Go to System Preferences -> Sound -> Sound Effects. Toggle through the effects and make note of the sound that your mystery application is playing. When you find it go to the terminal and type:
sudo fs_usage | grep "aiff"
Enter in the system password if asked.
Wait for the sound to get played again and then look at the terminal output. Look for the name of the sound file you noted in the sound effects and look all the way to the right. On the right you should see the application that played the sound file. Now simply go to that application and tell it to disable playing the sound file if possible.