Conditions for complete destructive interference

Steps:

• Fixed minima with zero displacement indicate stable interference pattern requiring coherence for consistent phase relation.
• Zero displacement at all times means complete destructive interference, not partial.
• Complete destruction occurs when path difference is odd multiple of λ/2 and amplitudes are equal.
• Unequal amplitudes or incoherence prevent zero minima at fixed points.

Why A is correct:

• Coherence ensures fixed phase difference for stable pattern; equal amplitudes allow total cancellation per superposition principle, yielding zero displacement.

Why the others are wrong:

• B: Unequal amplitudes cause partial minima, not zero displacement.
• C: Incoherence leads to fluctuating pattern without fixed minima.
• D: Lack of coherence and equal amplitudes prevents any stable interference.

Final answer: A