Superposition of Two Wave Pulses of Equal Amplitude and Opposite Phases Moving towards Each Other

Now consider two wave pulses of the SAME (equal) amplitude but OPPOSITE phase -- for instance, one an upward crest and the other an equal-sized downward trough -- again launched from opposite ends of a string towards each other. As before, each propagates independently while separated. But now, as they overlap, the resultant displacement at each point is the sum of one POSITIVE and one equal-magnitude NEGATIVE displacement, which cancel exactly. At the instant of perfect overlap, the resultant displacement is ZERO everywhere along the overlapping region -- this is DESTRUCTIVE interference, the wave energy momentarily appearing to vanish from view even though it is still present (carried, at that instant, entirely as kinetic energy of the medium rather than as visible displacement). Just as in the same-phase case, once the two pulses have cross …