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I'm a bit confused about how pulses can move away from each other, unaffected, after their 'meeting point'. Intuitively, I feel that if they meet, why don't they combine into one larger wave and move in the direction of the pulse with higher velocity? Or, if it is destructive interference, how can the pulses continue to move in their original directions with the same energy and velocity?

Also, in the destructive interference, how is the energy conserved? It seems as if the energy is lost in the 'cancelling' of the two waves.

Andi Gu
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If you are talking about pulses propagating as solutions of a wave equation, you have to consider that the wave equation is a linear partial differential equation. Therefore different solutions to this equation, like running "pulses" will combine in a linear manner, i.e., the different solutions will not influence each other. They just superimpose and continue running as if the other pulse was not there.

In a system where destructive interference occurs locally, there will be be constructive interference elsewhere so that energy will always be conserved.

freecharly
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  • Can you give a real life example of this happening? I understand the math behind it, but I'd like some intuition behind it (the reason pulses can go on seemingly unaffected after they meet) – Andi Gu Dec 02 '16 at 22:58
  • @Andi Gu - A simple example is a rope held at its ends by you and your friend. If you an your friend simultaneously hit the rope shortly with the other hand at the respective end, a wave pulse will propagate towards the other end superimposing and continuing to propagate unchanged in the middle of the rope. – freecharly Dec 04 '16 at 19:38