There are plenty of contributions in the physics literature on the subject of standing waves. What seems to be missing is an accessible, quantitative account of standing waves on a circular path at a level appropriate for undergraduate physics courses. In order to rectify this absence, a straightforward, concise, mathematical description of standing waves on a circular path is presented in terms of standard circular motion parameters.

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Videos of standing waves in a wire loop may be viewed at https://youtu.be/70OgGm2U9vU andhttps://www.youtube.com/watch?v=df3oJPi9_mg.
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Ref. 12, p. 20.
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22.
Generated using Mathematica 11.1.
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Generated using Mathematica 11.1.
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7A50.40-Bohr Model-Vibrating Circular Wire
,” University of Iowa Physics, https://instructional-resources.physics.uiowa.edu/demos/7a5040-bohr-model-vibrating-circular-wire.
28.
These differences are described in Ref. 9, p. 293.
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