Q.Draw a wave and indicate points which are

[!TLDR] On a displacement-distance sine curve, points a full wavelength apart are in phase, points half a wavelength apart are out of phase, and points a quarter-wavelength apart differ in phase by π/2. [!ANSWER] Same- …

Sketch a sinusoidal displacement-versus-distance curve (as in Fig 8.1(a)), with the wave travelling along +x. Mark a particle B at its positive maximum displacement (phase 90°/π/2). A particle F located exactly one wavelength λ further along, also at its positive maximum with velocity in the same direction, is IN PHASE with B (phase difference $2\pi^c$, i.e. effectively 0, since phase is only meaningful modulo $2\pi$). A particle D located exactly half a wavelength (λ/2) from B, at the corresponding NEGATIVE maximum, is OUT OF PHASE with B (phase difference $\pi^c$ = 180°) -- same magnitude of displacement but opposite sign, and oppositely directed velocity. A particle located exactly a quarter wavelength (λ/4) from B -- e.g. at the point where the curve crosses zero displacement, moving in a definite direction -- has a phase difference of exactl …

Use the phase-angle-vs-distance correspondence from section 8.2 (one full wavelength of separation = 2π phase difference) to locate points at …

Marking 'in phase' points as simply having the SAME displacement, without also checking their velocity DIRECTIONS match -- e.g. points at the same height on the rising and falling parts of the curve have equal displacement but opposite velocity directions, …