This is a Vanguard TV-2BU rocket, the U.S.'s first rocket specifically designed to launch satellites. As part of the Vanguard program, the Vanguard TV-2BU test vehicle was prepared for launch by the Martin Company on September 3, 1957. But due to a technical problem the mission was cancelled. The next launch opportunity was on June 22, 1959. However, the TV-4BU test version of the Vanguard was launched instead and orbited Vanguard 3.
Meanwhile, on March 17, 1958, the first successful Vanguard satellite was launched as Vanguard 1 atop a Vanguard TV-3BU rocket. The TV-2BU rocket was thus never used in the program but was essentially a duplicate of the Vanguard 1 vehicle and had the same markings. This TV-2BU was donated to the Smithsonian in 1958 by the Naval Research Lab.
This object is not on display at the National Air and Space Museum. It is either on loan or in storage.