Why does this video appear to show a wave with no trough? Do such waves exist?
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asked Jun 12, 2022 at 15:42
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3$\begingroup$ You might call it a pulse. You can easily send one along a rope. $\endgroup$– FarcherCommented Jun 12, 2022 at 16:12
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3$\begingroup$ I don't understand the downvotes on this question. This is a perfectly reasonable question. $\endgroup$– Emilio PisantyCommented Jun 12, 2022 at 20:21
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$\begingroup$ I agree with Emilio. $\endgroup$– user45664Commented Jun 13, 2022 at 16:50
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2 Answers
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Definitely what you can see there exists. It is an image of a real experiment on solitons in fluids. I think that most people will call it a wave. However, the equation satisfied by such a wave or soliton is not the ordinary wave equation, but a different differential equation. So if you call it or not a wave, it is a matter of convention, but its existence is a fact.
If you define something as a "wave" by saying that it satisfies the wave equation the problem is moved to "what do you call a wave equation" as there is no unique equation satisfied by all the "waves". I would not worry to much about names. The question of "is this really a wave" does not bring much benefit.
But you recognized that this is a peculiar type of wave and the first people to observe it were also thrilled to see it. It was first described at the beginning of the 19th century. Not that they did not exist before that time. There is at least on thread on this stackexchange about the general question "what do you call a wave"?
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1$\begingroup$ The fact that the experiment as shown (presumably!) shows a soliton which obeys a nonlinear differential equation is irrelevant. It is perfectly possible to build pulse solutions of the standard wave equation with identical features. $\endgroup$ Commented Jun 12, 2022 at 20:23
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$\begingroup$ Maybe your last sentence refers to this thread? The accepted answer there is dead wrong, but the discussion is valuable. $\endgroup$ Commented Jun 12, 2022 at 20:25
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$\begingroup$ The OP asked about the phenomenon in the image. My answer was addresing the question soI think it is relevant to the question as asked. Why is that so often people answer not the question asked but something that they assume the OP should have asked? I did not look for a specififc thread but I remember discussions along this line. I did not mean a specific answer in a specific thread. Just wanted to tell the OP that a search may provide som relevant (more or less) discussions. He can read your answer too, not just the accepted answer. $\endgroup$– nasuCommented Jun 12, 2022 at 21:36
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A wave has both crest and trough (undulating form) portions of the same amplitude and frequency. A wave with zero amplitude and zero frequency i.e. a monochromatic infinite straight line (if we are allowed to call it a wave!) will have no trough and compulsorily no crest.
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$\begingroup$ Your answer could be improved with additional supporting information. Please edit to add further details, such as citations or documentation, so that others can confirm that your answer is correct. You can find more information on how to write good answers in the help center. $\endgroup$– Community BotCommented Jun 12, 2022 at 16:56
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3$\begingroup$ A wave by definition is a propagating disturbance. No need for a trough. $\endgroup$– kricheliCommented Jun 12, 2022 at 20:19