FIGURE 17.5a has collapsed the nine graphs of Figure 17.4c into a single graphical representation of a standing wave. Compare this to the Figure 17.3 photograph of a vibrating string. A striking feature of a standing-wave pattern is the existence of nodes, points that never move! The nodes are spaced $\text{λ}\text{/}2$ apart. Halfway between the nodes are the points where the particles in the medium oscillate with maximum displacement. These points of maximum amplitude are called antinodes, and you can see that they are also spaced $\text{λ}\text{/}2$ apart.

FIGURE 17.5 The intensity of a standing wave is maximum at the antinodes, zero at the nodes.

It seems surprising and counterintuitive that some particles in the medium have no motion at all. To understand this, look closely at the two traveling waves in Figure 17.4a. You will see that the nodes occur at points where at every instant of time the displacements of the two traveling waves have equal magnitudes but opposite signs. That is, nodes are points of destructive interference where the net displacement is always zero. In contrast, antinodes are points of constructive interference where two displacements of the same sign always add to give a net displacement larger than that of the individual waves.

In Chapter 16 you learned that the intensity of a wave is proportional to the square of the amplitude: $I\propto A^2$. You can see in FIGURE 17.5b that maximum intensity occurs at the antinodes and that the intensity is zero at the nodes. If this is a sound wave, the loudness is maximum at the antinodes and zero at the nodes. A standing light wave is bright at the antinodes, dark at the nodes. The key idea is that the intensity is maximum at points of constructive interference and zero at points of destructive interference.