This is the AGM-76A, an air-to-ground version of the Falcon missile that usually appeared as an air-to-air weapon. The parachute cord strands attached to it were to see how the air flowed over the missile during aerodynamic tests. The short-lived AGM-76 concept was developed by Hughes Aircraft Company in 1966.
The AIM-47 air-to-air missile was to be converted into a fast, long-range missile called AGM-76 to destroy enemy surface-to-air missile (SAM) sites in North Vietnam before the launch aircraft came into the lethal zone of the SAM missile. But after the AGM-76 concept was approved by the Air Force, the U.S. Navy promoted an air-to-ground version of its existing Standard missile developed for this purpose, and Standard won. This object was donated to the Smithsonian in 1970 by Hughes Aircraft.
Transferred from the Hughes Aircraft Co.