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This is the wave by fans. Does it satisfy the wave equation?

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@Chris: I have nine questions. I am reviewing them and unfortunately I can accept answers in maybe in 2 or 3 of them. – Zeynel Oct 2 '12 at 0:25

With the football stadium wave, the thing is that each person acts individually and everyone behaves differently. If you assume they react all under the same conditions (e.g. they see their direct neighbor standing up), with equal reaction time (a key quantity here) and they all move up and down in the same manner (for example like one smoothed out cosine bump), then you can view it as a wave on a torus shaped grid, their seats being the grid points. I can't see which particular equation that system will fulfill though, if you make some sort of continuum limit.

This video is somewhat related (and also pretty cool). It gives a straightforward idea of the field concept, emerging through distinct living agents.

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I asked the question to investigate the problem of the motion of the wave in the field. In the case of the stadium wave there are no two distinct entities, wave and field, the field is made of elements and the elements’ motion appear as a wave moving in the field. The motion of the field is called the wave as in this from above Are all wave motion like this? – Zeynel Oct 3 '12 at 0:46
I would like to know examples of waves observed by physicists of both kinds; is there such a list? More specifically, examples of fields appearing as waves (no field/wave duality) as in the stadium wave and waves moving in a field. Is there even such a distinction? – Zeynel Oct 3 '12 at 0:48
@Zeynel: I think you never speak of a wave without there being an associated field. In some cases you might call the field a medium, but field here is really only a placeholder for that which can take different configurations and a wave is a particular one, dynamical in time. – NikolajK Oct 3 '12 at 20:46

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