With both ends free to move, the slinky can be used to show standing wave modes analogous to an open air column, like a flute. The fundamental mode has a node in the center, which can be seen clearly with the slinky.
If placed on a table with one end fixed, the slinky can also be used to demonstrate transverse waves and transverse standing waves, which can occur in all harmonics. The first four standing wave modes are shown.
Another useful visualization with the slinky is the fact that a traveling wave will reverse in phase upon encountering a fixed end. An incoming right pulse will reflect as a left pulse (see another example). There are analogies with light and other waves upon encountering reflecting interfaces.