Twenty Eleven – How do I create additional sidebars?

I am using the Twenty Eleven theme with a child theme applied (including a functions.php and index.php in my child theme folder).

I want to be able to insert different sidebars in the ‘Sidebar Template’ so that I can change the menus and widgets to match the context of the various pages (when I say ‘different’, I mean identical size and location, with a different name). As is stands now, if I put a ‘text widget’ in the sidebar with ‘Hello World’ typed in, then “Hello World’ appears on every page. I want the flexibility to put different menus and data in the sidebars as I choose.

Thank you.