Nodes and antinodes (definitions)
● VERBATIM — examined word-for-wordA node is a point on a stationary wave where the amplitude is zero; the two component waves always arrive there in antiphase. An antinode is a point where the amplitude is a maximum (equal to twice the amplitude of one component wave); the two component waves always arrive there in phase.
What this actually means
Amplitude, not displacement. A node is not a point that happens to be at zero displacement right now. It is a point whose amplitude is permanently zero, so the particle there is always at rest.
Every other particle on the stationary wave does oscillate. The amplitude simply varies with position, from zero at the nodes up to 2a at the antinodes.
The phase explanation is what earns the second mark. At a node the path difference from the two component waves is always a half-integer number of wavelengths; at an antinode it is always a whole number.
Boundaries fix where nodes go. A fixed end of a string and a closed end of a pipe must be displacement nodes; a free end of a string and an open end of a pipe must be displacement antinodes.
For sound in a pipe, a displacement node is a pressure antinode and vice versa. That is why the microphone in a resonance tube picks up the loudest signal at the closed end where the air is not moving.
Defining a node as a point of zero displacement, which is true of every particle twice a cycle. It must be zero amplitude.
Prove it — watch it be true
- Select the string system and mode n = 3 so three loops are visible.
- Turn on the N and A markers and confirm the marked nodes never move while the antinodes swing through the largest displacement.
- Place the probe exactly on a node and confirm the displacement readout stays at zero for a full cycle.