Trig method — no axis values
● VERBATIM — examined word-for-wordWhen x and λ can't be read: relabel the x-axis as a phase axis (1λ ↔ 360°). A particle at displacement y sits at angle given by sin θ = y/y₀ — at half amplitude, θ = 30°. Work out each particle's angle, subtract. The "hard" phase question is pure trig, not a new formula.
sin θ = y/y₀What this actually means
Some graphs give no numbers on the axes, only displacements as fractions of the amplitude. The trick: relabel the x-axis as phase, with one wavelength spanning 360°.
A particle at displacement y sits at the angle θ where sin θ = y/y₀. Half amplitude means 30°, not 45°, because the sine curve is steep near zero.
Find each particle's angle, subtract, done. The 'hard' phase question is O-level trigonometry wearing a wave costume.
Assuming half amplitude means 45° of phase — sin 30° = ½, so it is 30°.
Prove it — watch it be true
- Open the phase protractor and drag the marker to y = y₀/2
- The angle reads 30°, not 45°
- Drag a second marker, subtract the two angles: that is Δφ