The vertically suspended slinky is a system where variable tension, and variable mass density, combine to produce a simple solution for the longitudinal normal modes. The time taken for a longitudinal wave to traverse a single turn of the slinky is found to be constant for a variety of slinky configurations. For the freely suspended slinky this constant traverse time yields standing wave frequencies that depend only on the length of the hanging slinky and not on the material, radius, or stiffness of the slinky. Data, obtained by students in a laboratory setting, are presented to illustrate the application of these results.  

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