= Antinode
An antinode is a position of maximum oscillation <amplitude> in a <standing wave>. For $u_n=A\sin(n\pi x/L)\cos(\omega_nt+\varphi)$, the <antinodes> occur at
$$
x_j=\frac{(2j+1)L}{2n},\qquad j=0,1,\ldots,n-1,
$$
where the <amplitude> is $|A|$. They sit halfway between consecutive <nodes of a standing wave>. For the first <normal mode>, the sole <antinode> is $x=L/2$. It reaches zero <displacement> at a quarter <oscillation period> while moving fastest, which illustrates why an <antinode> is defined by oscillation <amplitude> rather than instantaneous height.
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