Stationary waves: identifying the incorrect statement

Steps:

• Stationary waves form from superposition of two identical waves traveling in opposite directions.
• Evaluate A: Particles between nodes have phase differences, increasing from 0 at one node to π at the next.
• Evaluate B: At antinodes, amplitude is twice that of each traveling wave due to constructive interference.
• Evaluate C: Node separation is λ/2, so wavelength equals twice the node spacing.
• Evaluate D: Antinodes exhibit maximum particle displacement over time.

Why A is correct:

• Between nodes, phase varies linearly, so particles do not oscillate in phase, violating the phase uniformity claim.

Why the others are wrong:

• B: Amplitude at antinodes is 2A, matching the statement for one wave's amplitude A.
• C: Wavelength λ = 2 × node separation, as nodes occur every half-wavelength.
• D: Antinodes have maximum oscillation amplitude, ensuring particle displacement.

Final answer: A