Coherence requires constant phase difference and matching frequency

Steps:

• Recall that coherence means waves maintain a fixed phase relationship over time for stable interference.
• Statement 1 (same frequency) ensures waves stay in phase sync, as differing frequencies cause drifting phase.
• Statement 3 (constant phase difference) directly provides the fixed phase relation needed for coherence.
• Statement 2 (same amplitude) affects interference intensity but not the coherence condition itself.

Why C is correct:

• By definition, two waves are coherent if they have the same frequency and constant phase difference, allowing predictable superposition.

Why the others are wrong:

• A: Amplitude equality is unnecessary for coherence; it only influences pattern visibility.
• B: Constant phase difference is essential; without it, waves cannot maintain coherence.
• D: Same frequency is required; mismatched frequencies lead to varying phase, destroying coherence.

Final answer: C