This boils down to one of two reasons (or a combination):
- CPU loaded at login when sound is played
- Some intrinsic problem with the Skype WAV files
Solution to (1) is to delay start OR temporarily elevate Skype priority
You can either delay the startup, as David Sousa/Marty Fried's answers indicate, OR you can temporarily elevate Skype's priority at startup to reduce any CPU contention issue.
This solution uses
nice/renice, and requires adding the specific command with
visudo (because only root can start processes with elevated priority). I'll expand on this later since the OP (Emerson) indicates this is not his problem -- Skype login sounds grainy even when he starts Skype after his computer has been idle for a few minutes.
Solution to (2) -- try changing the sound into a more standard format (resample)
If not, please try playing the Skype directory sounds in a regular player, and see if they still sound bad.