Final answer:
Two mechanical waves meeting with opposite displacements cause destructive interference, resulting in a wave with reduced or zero amplitude. Pure destructive interference completely cancels out the waves, creating no resultant wave.
Step-by-step explanation:
When two mechanical waves meet and have displacements in opposite directions from the equilibrium position, destructive interference occurs. Specifically, when one wave has a positive displacement and the other a negative one, their amplitudes subtract from each other. If the waves have exactly the same amplitude but opposite phases, they will cancel each other out completely, resulting in an amplitude of zero, known as pure destructive interference. This phenomenon is illustrated in Figure 16.37, where two identical waves are aligned crest to trough, neutralizing each other's effect.
The opposite of this would be constructive interference, where two in-phase waves add their amplitudes together, as shown in Figure 16.36. In such cases, if the initial waves have identical amplitudes, the resulting wave would have twice the amplitude but maintain the same wavelength.