I’ve been really annoyed at Skype for this weird behavior: When I was on a call, the audio worked fine. But when someone was calling me, I only got the small notification window but no ringing sound.
I couldn’t figure this out for a long time, but now I found a solution: Open the system-wide sound settings and unmute alerts/notification sounds. Now, you should get a ringing tone whenever somebody calls you.
This fixes one problem and creates a second one which I will fix below, but let me first give you some info on the origin of this behavior. When running on a system that uses PulseAudio, Skype doesn’t use the regular audio output methods for playing its notification sounds but plays the sounds through the audio notification channel. If you don’t like to hear system notifications such as log-in sounds et cetera and thus disable this channel in the audio settings, Skype doesn’t ring…
Fixing the original problem leaves us with a new one: If you don’t really appreciate the system notification sounds, you can configure the system to not play notification sounds without muting the notification channel. With Gnome 3, open the dconf-editor tool and go to org -> gnome -> desktop -> sound. Uncheck event-sounds. Done!
Now, you should hear a ringing sound if someone calls you, but no annoying system notification sounds.