Conditions for Stationary Wave Superposition

Steps:

• Stationary waves form from two oppositely traveling progressive waves interfering constructively and destructively.
• Matching frequency prevents the pattern from propagating, creating fixed nodes and antinodes.
• Equal wavelength ensures consistent interference intervals along the medium.
• Same speed, determined by the medium, allows proper overlap without distortion.
• Phase difference varies with position (Δφ = 2kx + φ₀) due to opposite propagation directions.

Why A is correct:

• Oppositely traveling waves have a phase difference that varies linearly with position x, not constant along the line, as derived from their phase terms (ωt - kx) and (ωt + kx + φ₀).

Why the others are wrong:

• B: Identical frequency is required for time-independent superposition and stationary pattern.
• C: Same wavelength follows from v = fλ with equal f and v, ensuring uniform nodes.
• D: Equal speed in the same medium is essential for the waves to maintain synchrony.

Final answer: A