Phase difference of 90° in transverse waves

Steps:

• Points X and Y separated by λ/4 have a phase difference of π/2 radians.
• Displacement at X: y_X = A sin(θ), where θ = ωt + φ.
• Displacement at Y: y_Y = A sin(θ + π/2) = A cos(θ).
• Analyze possibilities using trigonometric identities like sin²θ + cos²θ = 1.

Why A is correct:

• Both having zero displacement requires sin θ = 0 and cos θ = 0, which is impossible since sin²θ + cos²θ = 1 ≠ 0.

Why the others are wrong:

• B: Opposite directions possible (e.g., sin θ = 0.707, cos θ = -0.707).
• C: Same magnitude possible (e.g., |sin θ| = |cos θ| = √2/2 at θ = π/4).
• D: Same magnitude possible (e.g., |sin θ| = |cos θ| = √2/2 at θ = π/4).

Final answer: A