Pressure graphs — two flavours
● VERBATIM — examined word-for-wordΔp–x graph: centred on zero, positive at C, negative at R — λ/4 (π/2) out of step with the displacement graph. Absolute p–x graph: same shape but centred on atmospheric pressure — it can never start from zero (zero pressure = vacuum). Displacement wave and pressure wave differ in phase by π/2.
What this actually means
Two pressure plots exist. The Δp–x graph (variation from atmospheric) is a sinusoid through zero, peaking positive at compressions and negative at rarefactions. The absolute p–x graph is the same curve lifted to sit on atmospheric pressure.
Absolute pressure can never touch zero on these graphs, because zero pressure means vacuum. Sketching it from the origin is a giveaway error.
Displacement and pressure graphs sit λ/4 apart along x, which is a phase difference of π/2. Quote both forms: pressure peaks where displacement is zero.
Prove it — watch it be true
- Line up the s–x and Δp–x graphs with the guide lines
- Δp peaks sit exactly where s crosses zero: shifted by λ/4
- A quarter wavelength of offset is π/2 of phase