So you have a piece of string. Two people create a half wave at either end, one up and one down of equal magnitude. When they reach each other they will superimpose to create the sum of their amplitudes, X and -X producing 0. Freeze the string at this instant in time and it's completely flat, there is no longer a wave. So where does the energy go? And how can the two initial waves continue? The string isn't moving so what causes the wave to continue?
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$\begingroup$ Why do you say the string isn't moving? $\endgroup$– M. EnnsCommented Apr 20, 2017 at 11:06
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$\begingroup$ The energy is positive only, so, cant be cancelled. The waves are opposite in sign and are moving in opposite direction. During superposition, the energy is stored in as tension in string momentarily , which is released as waves travel further. $\endgroup$– Anubhav GoelCommented Apr 20, 2017 at 12:34
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The displacement might be zero but the string is still moving.
Have a look at this animation which shows this.
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$\begingroup$ I found it not enough to explain question. It was a bit low quality. (Though animation was good). Since, question is duplicate, I dont think you would edit your answer now. This can well be forgotten. $\endgroup$ Commented Jul 29, 2017 at 11:28