These instruments demonstrate the “communication of vibrations” between connected plates. This was a topic first investigated by the French scientist Felix Savart, in the 1820s. Savart experimented with a pair of identical glass disks that were connected by only a single glass rod. When the two disks were sprinkled with sand and the first one vibrated, both disks formed identical patterns.
Source: Steven Turner; Curator, Physical Sciences, National Museum of American History, Smithsonian Institution.
This kind of fork-shaped tube was used to study the motions of different parts of a vibrating Chladni plate. If the ends of the tube were held over two zones that were vibrating in the same direction, a sound would be heard, but if the vibrations were in opposite directions they would cancel each other out (interfere) and the sound would be greatly reduced.
Source: Steven Turner; Curator, Physical Sciences, National Museum of American History, Smithsonian Institution.