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The points of minimal displacement are called "nodes."

The points of maximal displacement are called "antinodes."

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Q: What are the relatively still points on a standing wave called?
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That point is called a 'node'. The point(s) of maximum amplitude, on the other hand, are called quite logically 'antinodes'. The wave is called a "standing" wave, not because it stands still; it does move vertically, but not horizontally. As a sidelight, a book from the golden age of science fiction (when such fiction was still related to science) by J.G. Ballard called Chronopolis postulated a space-time continuum structured as a standing wave surface, whereupon stable time is possible at the nodes.


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