Are there any copyright restrictions when adding music to a video?
In general, there are two rights to every song: sync rights and master rights. To use music over a video you must get permission from both rights holders. In order to determine who owns the rights to a recorded song, there are various websites you may use such as ascap.com and bmi.com. Once you’ve determined who owns the sync and master rights, you have to contact each copyright owner separately and ask for permission to use the song. This process may become complex (and expensive) where there is more than one songwriter.
Note: If you or your students are producing a non-commercial work, it may be that they can create and publicly post the work under the Non-Commercial User Generated Content right.