Constantly the music is cutting out when playing a mission. Sometimes it comes back to play a little part befor it's gone again. I already set compatibility to Win95 but that didn't help. I also applied the german patch following this instructions:
www.pcgamingwiki.com/wiki/Wing_Commander_IV:_The_Price_of_Freedom
But I don't know if that has something to do with this issue or if there is a general solution for that.

I know this issue is 3 years old at this point, but just in case anyone is still having this issue I figured I would chime in.
What fixed this for me was going into the actual install directory "GOGGAMES/WC4" or wherever you have installed it and changing the compatibility setting to WIN98 for the WC4DVD.exe file. I would just delete the shortcut that's placed on the desktop and make a shortcut directly to that exe file instead. It only seems to work if you launch the game from the exe and not from the original shortcut on the desktop. Hope this helps.