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I've avoided the use of the word "force" here, because I think that's not the right model, but correct me if I'm wrong. In describing a wave, the wave has peaks and troughs of equal distance, ceteris paribus - what is the limiting circumstance that causes the wave to return to the baseline from either direction, instead of spinning off into infinity?

Chris B. Behrens
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  • What kind of waves are we talking about? Water waves? Light waves? "Waves" are a linear phenomenon, so there is no limiting amplitude in terms of their theory. Once that linearity assumption doesn't hold, the behavior of physical systems changes dramatically, though. To speak of waves in that context becomes a bit problematic. Then it's better to think of either scattering or e.g. solitons and kinks. – FlatterMann Jan 17 '24 at 23:24
  • My question, I suppose, is a bit more general than this, but let's say EM waves. – Chris B. Behrens Jan 18 '24 at 01:47
  • Electromagnetic waves would have to reach extremely high classical amplitudes before vacuum polarization would begin to produce charged fermion pairs. This is also frequency dependent. Magnetar fields are believed to reach 10^11T, but because they have low frequency, the resulting electromagnetic wave still behaves pretty much in a "linear" fashion if we discount the fact that its energy density is 10,000 higher than that of lead. It is not known if nature can produce higher fields than that. – FlatterMann Jan 18 '24 at 03:21
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    Voting to reopen. This question does not need details or clarity. It is perfectly clear, and has a good answer below. – gandalf61 Jan 18 '24 at 15:25

2 Answers2

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What is the circumstance that limits the amplitude of a wave?

  1. The intensity (power per unit of area) of the wave is proportional to the square of its amplitude. So the amplitude of the wave is limited by the power that the source can produce.

  2. For EM waves propagating in a material medium (as opposed to in vacuum), high amplitude waves may excite nonlinear behavior in the material; for example, arcing or burning, and this may limit the magnitude of a wave that can propagate through the material without high losses.

what is the limiting circumstance that causes the wave to return to the baseline from either direction, instead of spinning off into infinity?

This is a different question entirely. If you think of a vibrational wave on a metal spring, there is a restoring force such that the greater the displacement of the spring from the neutral point, the greater the force pulling it back toward neutral. This part of your question seems to be asking what plays that role in an EM wave.

In the EM wave, what happens is that the electric and magnetic fields exchange energy. Changing electric field produces a magnetic field and changing magnetic field produces an electric field. Rather than try to make this clear in my own words, I'll quote Feynman:

How can this bundle of electric and magnetic fields maintain itself? The answer is: by the combined effects of the Faraday law, ∇×E=−∂B/∂t, and the new term of Maxwell, c2∇×B=∂E/∂t. They cannot help maintaining themselves. Suppose the magnetic field were to disappear. There would be a changing magnetic field which would produce an electric field. If this electric field tries to go away, the changing electric field would create a magnetic field back again. So by a perpetual interplay—by the swishing back and forth from one field to the other—they must go on forever.

Similarly to Feynman's argument here, if (for example) the electric field were to increase indefinitely, then that changing magnetic field would also produce an increased magnetic field strength. But the energy for that would have to come from somewhere --- it would have to draw energy out of the electric field for that to happen --- and the excursion of the electric field is limited by its energy being drawn away to form the magnetic field for the next cycle of the wave.

The Photon
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  • Take my upvote for pinpointing the essence of the question. I think it is important to point out to the OP that waves do not just exist out of nowhere. The waves we see are wave solutions to some DE that has to be obeyed. Deviations from baselines are counteracted by restoring forces. – naturallyInconsistent Jan 18 '24 at 03:07
  • @naturallyInconsistent This is where relativity throws a giant wrench, though, isn't it? The "restoring force against some background" picture works for acoustic waves and water waves, but not for electromagnetic waves and that makes their quantitative behavior, apart from some shallow similarities, very different. – FlatterMann Jan 18 '24 at 04:44
  • I did upvote this, but I think you gave another example of Feynman's rather shallow teaching. There are no "electric fields" that are independent from "magnetic fields". Which components we see depends on the relative velocity between the sources and the observer. In my opinion the high school method of introducing electrostatics first plays a cruel joke on student's minds. Even well known college textbooks keep pretending chapter after chapter that treating the static fields as if they were Galileo invariant is a sufficient idea, which leads to wrong approximations galore. – FlatterMann Jan 18 '24 at 04:50
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    @FlatterMann, fair, but at the same time you have to walk before you can run. If we tried to start out freshman year (or in high school or the local equivalent) teaching tensor calculus (a subject that I've managed to avoid myself, despite having an engineering PhD) we'd lose nearly all the students due to lack of motivation. I answered the question assuming it was asked in the context of classical electromagnetics. – The Photon Jan 18 '24 at 17:09
  • This is slightly off topic, but the older I get the more I question if teaching science from a 19th century perspective is the right thing to do. I did have to learn scalar products at the high school level, by the way, and even the cross product was discussed and used for torque and angular momentum. I had been taught most of basic linear algebra except for the concept of Eigenvalues and Eigenvectors, so tensor algebra would have been perfectly within reach, even at the high school level. I honestly think we should give up teaching Euclid and teach serious geometric algebra, instead. – FlatterMann Jan 18 '24 at 21:50
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A mechanical wave - be it at the boundary of two media such as water-air or in a medium such as a bell - is always bound to the "constitution" of the media. This includes the elasticity or viscosity of the solid or liquid. If the cohesive forces are exceeded, the amplitude of the wave - which is proportional to the force acting on it - is destroyed. In addition to the magnitude of the force, the frequency of the impact also plays a role. This is not the case with an impact, but there are plenty of examples where the force also acts periodically.

The story is completely different for electromagnetic waves. Here, the amplitude is associated with the energy of the wave. The EM wave has a frequency and two components that are perpendicular to each other in a vacuum, consisting of the electric and magnetic components. However, the expansion of these components is assumed to be infinitely extended.

HolgerFiedler
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