wp query custom taxonomy of custom post type

I have created a custom post type called faculty. I have also created a custom taxonomy called departments. I am trying to create a archive-faculty.php page in order to set a custom loop to loop through this new custom post type.

I have the basic loop set up which will show all faculty members. I want to be able to only show faculty members of the current department.

I was hoping the url could be http://www.mysite.com/facutly/department where department is the current department. Is it possible to have http://www.mysite.com/posttype/taxonomy as the url. If so how, and if so how can i get the taxonomy that is in the url in order to use it in WP_Query

Thanks