C and R live at ZERO displacement
● VERBATIM — examined word-for-wordOn the displacement–distance graph of a sound wave, compressions and rarefactions all sit at equilibrium (zero-displacement) positions — never at the peaks. The lecturer makes the class chant this; it is the #1 weak-student error.
What this actually means
A compression is where neighbours have closed in from both sides. The particle at its centre has been shoved equally from the left and from the right, so its own displacement is zero.
Peaks of the displacement graph are particles far from home, but their neighbours moved with them, so nothing is bunched there. Distance from equilibrium and crowding are different things.
So on the s–x graph, every C and every R sits on the x-axis. Chant it like the lecture did: compressions and rarefactions live at zero displacement.
Placing a compression at a displacement peak — C and R sit at zero displacement.
Prove it — watch it be true
- Follow the guide lines from each C and R halo down to the s–x graph
- Every one lands on a zero crossing, never a peak
- Pause and check a displacement peak: the particles there are evenly spaced