Taking into consideration the given scenario, I suppose that the music professor used the MP3 music download with fair intention. However, the professor should not have posted the clip of the excerpt on his/her website.  The following explanations, in consideration of the four fair use factors, support my opinion:

The purpose, character and nature of the use.  The professor downloaded the MP3 file in order to extract a clip which he needed to use for a class discussion. This is considered fair use as the work is to be used for teaching, criticism and comment. It may also elicit in his students the creativity to create new work with a different purpose from the original material. The professor intended to use this in class, making the nature of the use non-commercial and non-profit.

The nature of the copyrighted work.  The copyrighted work was creative music, in MP3 format downloaded from the Internet. As it was downloaded from the Net, the piece can be taken to mean that it was a published work.

The amount and importance of the borrowed portion to the entire copyrighted material.  The professor extracted a 30-second clip from the downloaded MP3 music file.  This is most likely less than the eighth part of the entire work which was intended as a teaching aid for a class discussion. However, the professor should not have posted the clip on his website as this may constitute an infringement of fair use.  Fair use allows for the clip to be used in a classroom only.  If his website is available only to his students, then it will not be infringement.

The effect of use on value of copyrighted work.  The use of a clip of the original work for teaching purposes does not do any potential damage to the market value of the work nor may prejudice the sale of the original work thus diminishing the profits of the copyrighted work.