Custom post type by itself can not do what you want. It’s just another way to organize content on your website.
For the post type to do something extra your theme must include a page template targeting the specific post type with an extra piece of code which loads a media player to the page (with the target audio file either from a url in the content of the post or a custom field).
But the most simple way to manage this is to use a media player plugin (this one for example).
The plugin already includes the “custom media player code” you need to the page and allows you to add the media player via a simple shortcode in any post you want.
You can still use the custom post type for organization, but all you have to do is add the shortcode in the content of the post.
