Propagation of Waves - Exploring Mechanical & EM Radiation

[Rainbow]

Suppose we have a stretched string, with one of its end fixed at a wall. Now if we just jerk the string(up and down), we get a mechanical wave, i.e. the disturbance caused by us at one end of the string travels to the other end. Now the question is, how and why does the disturbance travel through the string. All we do is just jerk the end of the string up and down, so what makes that disturbance travel along the string(perpendicular to the direction of the force we apply).
And now I would like to extend this to the electromagnetic waves. EM radiation consists of electric and magnetic oscillations. But how and why do these oscillations travel forward.

 

[jtbell]

All we do is just jerk the end of the string up and down, so what makes that disturbance travel along the string(perpendicular to the direction of the force we apply).

The molecules of the string exert attractive forces on their neighbors. These are the forces that keep the string or any other solid object together. So when the molecules at the end of the string move up and down, they drag their neighbors along (with a slight delay), which in turn drag their neighbors along (with a further slight delay), etc.

EM radiation consists of electric and magnetic oscillations. But how and why do these oscillations travel forward.

According to Maxwell's equations, changing electric fields produce magnetic fields, and changing magnetic fields produce electric fields, as I mentioned in a previous thread that you started.

 

[Rainbow]

The molecules of the string exert attractive forces on their neighbors. These are the forces that keep the string or any other solid object together. So when the molecules at the end of the string move up and down, they drag their neighbors along (with a slight delay), which in turn drag their neighbors along (with a further slight delay), etc.
According to Maxwell's equations, changing electric fields produce magnetic fields, and changing magnetic fields produce electric fields, as I mentioned in a previous thread that you started.

Like you explained, how the mechanical wave travels, can you kindly explain how these changing electric and magnetic fields in an EM radiation travel from point A to point B. I mean, if I'm not wrong, the changing electric field induces a magnetic field in the direction perpendicular to it, and the changing magnetic field induces an electric field. But these fluctuations should take place at the same point. What makes this effect propagate?

 

[jtbell]

If you look at it strictly pointwise, then according to Maxwell's equations (see the Hyperphysics pages that I linked to in my post in the other thread), the rate at which the electric field varies with time at a point gives you the rate at which the magnetic field varies with position at that point (not the value itself of the magnetic field). You get a similar relationship if you switch the electric and magnetic fields.

If you're looking for a mechanical, causal explanation behind Maxwell's equations, I don't think you'll find one that's generally accepted among physicists, at least not in the context of classical electrodynamics. In that context, Maxwell's equations are fundamental "givens" just like Newton's laws of motions are fundamental "givens" in classical mechanics. You'd be asking in effect, "why are Maxwell's equations the way they are?" which has about as much of an answer as "why are Newton's laws the way they are?"

 

[Rainbow]

Well thanks for the explanation. But I'll take some time to actually visualise the whole thing and then understand it.
And as you said something about the "fundamental laws" being the way they are, do you think we might be able to find some even more fundamental theory which will actually explain why these fundamental theories are the way they are? I mean is it what the "theory of everything" all about?

 

[Claude Bile]

But these fluctuations should take place at the same point. What makes this effect propagate?

It propagates in a very similar manner to the string case. If the electric field strength at some point were to increase, the field strength at surrounding points must also increase because nature demands that E and B fields must be continuous. This is somewhat analogous to the molecules of the string yanking their neighbours.

And as you said something about the "fundamental laws" being the way they are, do you think we might be able to find some even more fundamental theory which will actually explain why these fundamental theories are the way they are? I mean is it what the "theory of everything" all about?

Pretty much, yes. Will people find such a theory? Probably, given time. Hopefully within my lifetime!

Claude.

 

[Rainbow]

nature demands that E and B fields must be continuous.

Can you please explain this part.

 

[Claude Bile]

Continuity is a property of a mathematical function that basically says that the function doesn't leap suddenly from one value to another, there is always a smooth transition. For example, a continuous function, would not jump suddenly from 0 to 1 - instead it would pass through every possible value between 0 and 1.

E and B fields must be continuous. If this was not the case, discontinuous jumps would be permitted, which would result in unbounded (or infinite if you like) gradients, which implies that anything that depends on a spatial derivative of E would also become unbounded and so on.

Hand-waving aside, E and B fields are always observed to be continuous, and many useful laws which we observe to hold true such as Snell's law and the laws of total internal reflection, waveguide modes and so forth are all consequences of continuity conditions for E and B.

Claude.

 

[Rainbow]

Can you please explain in details, that at a particular instant, what happens at the front end of an EM wave as it travels forward.

 

[Claude Bile]

I'm not sure what details you're looking for exactly, I could go into a tirade about the time domain of a wave-packet, but I get a feeling that is not what you are looking for. Are you looking for some kind of "increase in E at point x causes an increase in E at point y" type explanation similar to the string case?

Claude.

 

[Rainbow]

Are you looking for some kind of "increase in E at point x causes an increase in E at point y" type explanation similar to the string case?

Claude.

Something like that Sir.

 

[Claude Bile]

Okay, well the "increase in E at point x causes an increase in E at point y" type explanation is not a natural explanation for an EM wave as it is for the string case. This is because the string case represents a wave that is a displacement from equilibrium. The displacement at X causes a displacement at Y argument is a natural explanation because the rope being displaced physically "yanks" via the application of force nearby sections of rope, causing them to be displaced as well.

The case of an EM wave however does not marry itself well to this type of explanation because various points in empty space are not coupled in the same way two points on a rope are. Instead, consider what causes a change in E at some point. Take the following scenario;

Oscillating Charge --------------X---------------Y.

A charge oscillates causing a variation in E at both X and Y, however this variation is not instantaneous due to relativistic speed limits. The oscillating E field will be "felt" at point X before it is "felt" at point Y, but that does not mean that the oscillation at point X causes the oscillation at point Y. I hope you can see how this is distinct from the rope case.

Claude.

 

[premagg]

See it from energy point of view.U provided some energy,where will it go??