Here's what happens:
* The amplitudes cancel out: Since the crest (positive displacement) of one wave and the trough (negative displacement) of the other wave have the same magnitude but opposite signs, they effectively cancel each other out at that point.
* No resultant displacement: The particle at that location will experience zero net displacement, meaning it remains at its equilibrium position.
* Minimum intensity: The intensity of the wave, which is related to the square of the amplitude, is minimized at the point of destructive interference.
In other words, at the point where the crest of one wave meets the trough of the other, the waves effectively "erase" each other, resulting in no wave disturbance.
This phenomenon is a fundamental concept in wave physics and has applications in various fields, including optics, acoustics, and electronics.
