What condition must be met for destructive interference to occur in waves?

Destructive interference occurs when two waves meet in such a way that they cancel each other out. For this to happen, the condition that must be satisfied is that the difference in path length between the two waves should be an odd multiple of half the wavelength. This means that if one wave is at a peak (crest), the other should be at a trough, leading to a net amplitude of zero.

When the difference in path length is a multiple of half the wavelength (such as one-half, one-and-a-half wavelengths, etc.), the two waves are perfectly out of phase. This results in the peaks of one wave coinciding with the troughs of the other, leading to cancellation. Therefore, the correct answer highlights this specific condition necessary for achieving destructive interference.

The other options present conditions that do not align with this principle. For example, if a wavelength is twice the distance traveled, it describes wave travel but does not pertain to interference specifically. The requirement of equal amplitudes, while it may facilitate maximum destructive interference, is not strictly necessary, as waves of different amplitudes can still interfere destructively. Lastly, waves being in phase is actually a criterion for constructive interference, not destructive, thus highlighting why the chosen answer is accurately aligned