Sec. 106 (2) grants the copyright owner the exclusive right "to prepare derivative works based upon the copyrighted work."
Rule of Thumb: You must ask for copyright permission from the copyright owner to make a derivative work.
A license must be obtained from the copyright owner of a musical composition to "synchronize" a recording of the composition to the film, video, images, etc.
The key words here are public television, short excerpts, & documentary. Under Sec. 107, Fair Use - the station can broadcast a tape of a documentary film about a musical group using short excerpts from some of their songs. (Up to 10% or 3 minutes of a program or copyrighted motion media work may be copied, otherwise written copyright permission must be obtained or purchase of the work made.) Any more than this and permission would need to be obtained.
Fair Use allows for:
Digital copying of scores & sound recordings for preservation ONLY may be allowed. The sound collection may be digitized and made available to students only within the library's viewing area-study carrels, etc. The library may not distribute these recordings over the Internet to the world at large. They must be made available for student use only.
It depends on the motivation for making the copy and the extent of the copying.
Rule of Thumb: Copying for the purposes of performance is prohibited. Emergency copying for an imminent performance is allowed, so long as the copy is replaced by a purchased copy in due course.
While the original composition was made over 100 years ago, the arrangement used by John Tesh is new and protected by copyright. The instructor should obtain permission to play the song in class.