Phase within and across loops
All particles between two adjacent nodes oscillate in phase with each other, reaching their extremes and passing through equilibrium at the same instant, although their amplitudes differ. Particles in adjacent loops oscillate in antiphase, that is π rad out of phase.
What this actually means
This is the fastest way to tell a stationary wave from a progressive wave on a diagram. In a progressive wave, phase changes continuously with position. In a stationary wave, phase only takes two values, and it flips as you cross a node.
Only two answers are ever possible in an exam: 0 rad or π rad. Count how many nodes lie between the two points. Even number of nodes means in phase, odd number means antiphase.
In phase does not mean equal amplitude. Two particles in the same loop, one near the node and one at the antinode, move together but with very different sizes of swing. Students confuse the two constantly.
The reason for the flip is the sign of the envelope. The standing-wave amplitude term changes sign every half wavelength, so particles on either side of a node are always moving in opposite directions.
A neat way to see it: pick the instant of maximum displacement and look at the snapshot. Particles in one loop are all above the axis while all those in the next loop are below it.
Saying particles between adjacent nodes have the same amplitude because they are in phase. Same phase, different amplitude.
Prove it — watch it be true
- Select the string with mode n = 3 and place the two probes inside the same loop.
- Confirm the phase readout says 0 rad and both traces peak at the same instant.
- Drag one probe across a node into the next loop and confirm the readout jumps to π rad with the traces mirrored.