Notification Center is a great addition to OS X Mountain Lion but the alert sounds can be pretty annoying if you have a lot going on. Rather than muting all system audio to hush the constant chiming, you can directly silence notifications on a per-app basis.
- Open System Preferences from Apple menu and click the “Notifications” menu
- Select apps from the left and uncheck the “Play sound when receiving notifications” box
- Repeat for every app you want to silence