Why are nodes and nodal sets called this way?

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Nodes of standing waves are points where they are zero. Generally, nodal sets of Laplacian eigenfunctions are the sets of points where they are zero.

Why is this the name for them (that is, why is the English word "node" used)?

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What does a node look like? Let Google be your friend and search for Pictures of nodes in waves or more general: Pictures of nodes, and find some waves between these.