Phase difference determines wavelength in progressive waves

Steps:

• Phase difference φ = 2π d / λ, where d = 0.25 m and φ = 2π.
• Substitute: 2π = 2π (0.25) / λ.
• Solve for λ: λ = 0.25 m.
• Wave speed v = f λ = 10 × 0.25 = 2.5 m s⁻¹.

Why A is correct:

• Phase difference of 2π means the points are separated by exactly one wavelength (λ = d), so v = f λ = 2.5 m s⁻¹ by the wave speed formula.

Why the others are wrong:

• B: Requires λ = 1 m (v = f λ = 10 m s⁻¹), implying φ = π/2 for d = 0.25 m.
• C: Requires λ = 2 m (v = 20 m s⁻¹), implying φ = π/4.
• D: Requires λ = 4 m (v = 40 m s⁻¹), implying φ = π/8.

Final answer: A