Why do mechanical and EM waves in the same way?

[terahertz]

Mechanical waves (sound, water waves) and EM waves both undergo diffraction. But the actual physical processes involved in the two are totally different. EM waves are produced by accelerated charges while mechanical waves are tiny displacements of molecules of the medium in which the wave is propagating? Isn't it strange that these two completely different phenomena both undergo diffraction?

 

[terahertz]

Sorry, typo in the title. I meant, why do they diffract in the same way.

 

[UltrafastPED]

"Wave" is a mathematical abstraction; to fit this model the phenomenon must obey the wave equation. The other properties are follow from the mathematical properties of the wave equation: refraction, reflection, diffraction ...

So if the physical phenomenon is a good match for the mathematical srructure - then the rest follows. It is sufficient to establish that you have a wave.

This is one good example of mathematics as the language of physics.

 

[ZapperZ]

Mechanical waves (sound, water waves) and EM waves both undergo diffraction. But the actual physical processes involved in the two are totally different. EM waves are produced by accelerated charges while mechanical waves are tiny displacements of molecules of the medium in which the wave is propagating? Isn't it strange that these two completely different phenomena both undergo diffraction?

Please note that the wave description only describes the behavior/property of the wave. It has nothing to say about how the wave was generated! So it shouldn't be surprising that these can be very different, i.e. it shouldn't be "strange", since that has never been part of what it describes.

It only looks strange if you have made a self-imposed criteria beyond what it can describe on how a wave should be generated.

Zz.

 

[terahertz]

Thanks for your replies, UltrafastPED and ZapperZ. Let me pose my question slightly differently. The wave equation in electromagnetics is derived directly from Maxwell's equations. Therefore, if diffraction of EM waves is explained on the basis of the wave equation, then it should also be possible to get the same result directly from Maxwell's equations (without bringing in the wave equation). Now, as Maxwell's equations tell us that EM waves are produced by accelerated charge, is it not be possible to trace the origin of the diffracted wave also to accelerated charge somewhere?

 

[ZapperZ]

Thanks for your replies, UltrafastPED and ZapperZ. Let me pose my question slightly differently. The wave equation in electromagnetics is derived directly from Maxwell's equations. Therefore, if diffraction of EM waves is explained on the basis of the wave equation, then it should also be possible to get the same result directly from Maxwell's equations (without bringing in the wave equation). Now, as Maxwell's equations tell us that EM waves are produced by accelerated charge, is it not be possible to trace the origin of the diffracted wave also to accelerated charge somewhere?

The wave equation is rather general. It has a mathematical form. And if you have studied mathematics at any detail, you will realize a very fundamental "habit" of mathematics and mathematicians, whereby when you find a new problem, and you can reduce it to something that you have seen before, then ALL mathematical rules and outcomes of that known and familiar form also apply to that new system.

It is why, for example, that we have a Gauss's law equivalent of gravitational field, and why such a forum is useful for gravity. Once I've reduced the classical gravity into such a form, then I don't have to "relearn" or "resolve" it, because I already knew what the electrostatic version of this form does.

The same can be applied to solving for the EM wave using Maxwell equations. All I did was to play around with those equations, and I end up with the form that resembles the known wave equation. Then what I did was simply to apply all the mathematical and physical outcomes of what I know a standard wave equation is able to produce. And I can do the same when I solve for the wave in water, on the vibrating membrane of a drum, etc...etc.

But what the GENERAL wave equation can't do is tell you what generated that wave. This is because such a question is no longer a general question, but rather a specific question applicable to that specific phenomenon. Such an information is not contained in the wave equation. In fact, just by writing down the EM wave equation after you manipulate Maxwell equations, I don't see how you can tell if the EM wave was a result of accelerated charges or from atomic transition. This information may be obtained from another Maxwell equation, but it is certainly not found in the EM wave equation.

If you still disagree with this, then I'd like to see you write the general wave equation for EM radiation, and show me how you arrive at what you are thinking of. That, to me, is the only way to produce a convincing argument.

Zz.