Node

A node is a point on a standing wave whose displacement is always zero, because the two counter-propagating waves cancel there at every instant. Adjacent nodes lie half a wavelength apart.

AP Physics 2 EK 14.6.B.1.i: a node is a point on the standing wave where the amplitude is always zero. Permanently zero, not zero at one instant, which every point on any wave is twice a cycle.

Half a wavelength apart. Exactly one antinode sits between two neighboring nodes, so the node-to-node spacing is λ/2\lambda/2. That geometry is where the whole harmonic series comes from: a string of length LL with a node forced at each end can only hold λn=2L/n\lambda_n = 2L/n for whole-number nn.

Where the boundary puts them. A fixed end of a string, or the closed end of a pipe, has to be a node; a loose end or an open end has to be an antinode. EK 14.6.B.1.iii lists those four regions as the common ones. Count nodes and antinodes off the diagram before reaching for any formula, because the diagram fixes the wavelength and the wavelength fixes everything else.

A node is not a dead spot in the medium. The displacement is pinned at zero, but the string is there and it is under maximum strain. What is true is that no net energy crosses a node in an ideal standing wave, which is another way of saying the pattern carries nothing along the string.

Nodes also appear in interference patterns away from standing waves, at points where two sources arrive exactly out of step (destructive interference).

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