First, change your Finder settings to allow you to see file name suffixes. You'll be amazed at what you are not seeing. Finder->Prefs->Advanced->check the "Show all filename extensions" choice. It can often be helpful to know this information when trouble-shooting. You can change the setting back later, of course.

Second, tell us exactly how you "recorded" the CD on your wife's Mac.
Third, tell us what the suffix is on the 'music' you transferred to your Mac.