All of the following are true EXCEPT:

• A. Two Waves With Identical Frequencies Must Interfere Constructively
• B. Constructive Interference Is Associated With Waves That Are In-Phase
• C. Out-Of-Phase Waves Interfere Destructively
• D. Waves Of Different Frequencies May Exhibit Both Constructive And Destructive Interference At Different Times

Answer: (A)

Interference depends on how the waves line up in time, not just how fast they’re traveling. If two waves have the same frequency, that doesn’t force them to reinforce each other all the time—what matters is their relative phase. If they happen to be in phase, their peaks line up and you get constructive interference. If they’re opposite in phase by 180 degrees, their peaks meet troughs and they cancel, giving destructive interference. So the idea that identical frequencies must interfere constructively is not correct.

Constructive interference, by definition, occurs when the waves are in phase—crests align with crests and troughs with troughs—so their amplitudes add. That’s why in-phase waves reinforce each other.

Out-of-phase waves interfere destructively because their peaks and troughs are opposite; when their amplitudes subtract, you can get reduced amplitude or complete cancellation, especially if the waves have similar amplitudes.

Waves of different frequencies can show both constructive and destructive interference, but not all the time in a fixed way. The relative phase between two frequencies changes over time, so periods of reinforcement can alternate with periods of cancellation. This often produces a beating pattern, where the overall amplitude waxes and wanes as the waves drift in and out of phase.

So the only statement that isn’t generally true is that two waves with identical frequencies must interfere constructively.