= Node
{disambiguate=physics}
{wiki}
= Node of a standing wave
{synonym}
= Nodes of a standing wave
{synonym}
A node of an ideal <standing wave> is a position whose oscillation <amplitude> is zero: its <displacement> stays zero for all time. For a nontrivial <normal mode> $u(x,t)=\phi(x)q(t)$, this means $\phi(x)=0$. A momentary zero caused by $q(t)=0$ does not make every position a node. In more dimensions the zeros of a <mode shape> can form curves or surfaces.
For the $n$th <normal mode> of a uniform fixed-end <wave equation on a string>, the <nodes of a standing wave> are
$$
x_j=\frac{jL}{n},\qquad j=0,1,\ldots,n.
$$
There are $n+1$ <nodes of a standing wave> including the two endpoints, and $n-1$ interior ones. For $n=3$ and $L=1\,\mathrm m$, they lie at $0$, $1/3$, $2/3$, and $1\,\mathrm m$. Each remains stationary through every snapshot in the <normal mode> diagram; an <antinode> instead marks a maximum oscillation <amplitude>. https://openstax.org/books/university-physics-volume-1/pages/16-6-standing-waves-and-resonance[OpenStax, University Physics Volume 1, Section 16.6]{ref}
Back to article page
