Microsoft Tip: Turn Off Web Based Skype Notification Sounds
Paul Thurrott's tip of the week on Windows Weekly 501 is that you can now turn off notification sounds on the web version of Skype. This is especially useful if you like to keep Outlook Mail open in your browser, while also having the desktop version of Skype running. Since Skype is always running in the web client, even if you turn off the desktop notification sounds, you'll still get them through the browser. Microsoft just fixed this last week.
To disable these sounds, simply open Outlook.com or OneDrive in a browser window, click the Skype button at the top, and click Settings. Select Notifications in the Settings pane, and you'll see a Sound toggle.