.add ()?

We have created .add() in playlist.js as a method to the prototype of Playlist:
function Playlist() { ... }

Playlist.prototype.add = function(song) {
this.songs.push(song);
};

We could have created .add() as a method to the Playlist constructor and it would work totally fine like this:
Playlist.add = function(song) {
this.songs.push(song);
};

But, if you do that objects created from Playlist by issuing "new" will have its own memory allocated to store .add() method while those objects essentially use the exact same method.

One way to resolve this is to create add() function that can be assessed globally and let Playlist refer to this function for the .add() method:
function add(song) {
this.songs.push(song);
}

function Playlist() {
this.songs = [];
this.nowPlayingIndex = 0;
this.add = add;
}

But then the add() function is not meant to be used by other than a Playlist object, so you contain it within the context of Playlist by putting it as a method of Playlist prototype.