Whether in a DVD or streaming format, permission is not needed to perform music or film in a face-to-face classroom due to copyright’s Title 17 U.S. Code § 110(1) that requires the following:

•     Performance occurs in the course of face-to-face teaching activities of a nonprofit educational institution;
•     in a classroom or similar place devoted to instruction;
•     with a pedagogical purpose;
•     via a lawfully made copy.

All four provisions must be met for the exception to apply: face-to-face, in a class, with a pedagogical purpose, and with a lawful copy. At WashU, a lawful copy does not include personal rentals or burned copies.

It’s up to the instructor to comply with copyright depending on whether a course is face to face or hybrid/virtual. Permission may or may not be needed for an online or hybrid class showing of a film under the TEACH Act or Fair Use. While the TEACH Act amendment (§110(2)) applies to material transmitted via course delivery systems like Canvas and extends it to an online, digital environment, it isn't clear or helpful when it comes to remote teaching and learning due to its serious limitations: only reasonable and limited portions of a dramatic work, musical, opera, commercial film, or music video can be shown. 

You can’t show an entire movie or musical work online. If you limit audio and video use for your course to very brief clips, you may be able to include those in lecture recordings or live casts under fair use.

• Permission from the copyright holder is required if you want to use more of the work than a fair use analysis would support.
• Permission from the copyright holder is required if the work is governed by a license that prohibits your proposed use without permission.

Obligations of the instructor under the TEACH Act include that the performance or display...

•     is made by or under the supervision of an instructor.
•     is directly related and integral to the class content, not ancillary like Reserves.
•     is made solely for and limited to students officially enrolled in the course.
•     is not available for longer than the class session.
•     includes reasonable controls to prevent copying and retention of the work. (Which is why streaming is suggested for video.)    

For media use longer than brief clips, you may need to have students independently access the content outside of your lecture videos. This does not require permission. The University Libraries subscribe to licensed streaming video content that instructors can link to for their courses and also have subscriptions to a significant set of streaming audio options for WashU users.