This is a spare nozzle for the original James H. Wyld regeneratively-cooled rocket motor. It thus probably dates to 1938. Wyld's motor was first tested on 10 December of that year on the American Rocket Society's Test Stand No. 2 at New Rochelle, New York.
The object was found in the collection but has a tag on it in the handwriting of John Shesta, who, with Wyld, Lovell Lawrence, Jr., and Hugh Franklin Pierce, founded Reaction Motors, Inc. (RMI) in December 1941, shortly after the U.S. entered World War II. Based upon Wyld's regeneratively-cooled motor, RMI subsequently developed JATO (Jet-Assisted-Take-Off) rocket motors, as well as rocket motors for missiles and the famous 6000C-4 motor that powered the Bell X-1 rocket research aircraft that broke the sound barrier in 1947. It was found in the Smithsonian collections, but very likely was a gift of the Reaction Motors Division of Thiokol Inc.
This object is not on display at the National Air and Space Museum. It is either on loan or in storage.