That's a problem with some copies of the game. You have to edit your fallout2.cfg file using notepad. Under the (sound) section find the lines music_path1= and music_path2= and make sure they are directed to the correct folders containing the music. Because for some reason, there are actually TWO sound folders (Fallout 2\sound\music) and (Fallout 2\DATA\SOUND\MUSIC). So you have to find the one that contains all the .ACM files and direct the music_paths there.
Hope I explained it well enough. Post again if you have any problems.
EDIT:
By default, the game's music files should be kept in FALLOUT 2\DATA\SOUND\MUSIC
In the .cfg file set music paths to:
music_path1=data\sound\music\
music_path2=data\sound\music\
That should fix the problem unless the files are kept somewhere else.