A video of this demonstration is available at this link.

This machine has three sections. The section at left has 72 18-inch-long metal rods soldered at intervals of 0.5″ to a spring steel wire running its length. The section at right has 72 nine-inch-long rods similarly soldered to a wire that runs its length. The section in the middle has 47 rods, whose lengths change gradually from 18 inches at one end, to nine inches at the other, fixed as in the other sections to a wire that runs the length of the section. Because the speed of a wave traveling along the machine depends on the moment of inertia of the rods, a wave travels faster through the section with 9-inch rods than it does through the section with 18-inch rods. Because of this, if you connect these two machines directly together, when you send a pulse from either end of the system, where the two machines are joined the pulse is partially transmitted and partially reflected. When you insert the middle section and connect all three sections together as shown, a pulse sent from either end of the system travels smoothly, with no reflection or loss between sections, through the length of the system. The units at the front edge of the table are strip lights, each of which has an ultraviolet fluorescent tube (“black light”), whose output excites the phosphor that is on the tips of the rods, causing them to glow. This makes it easier to see the motion of pulses or waves.

The page for demonstration 40.60 -- Transverse wave machine with free or fixed end, describes both the machine with 18-inch rods and the one with nine-inch rods in greater detail, and includes tables of frequencies of the first eight half-wavelength harmonics, and of the first six odd-quarter-wavelength harmonics, for both machines.