Wave on a string, something like E and B?

[Spinnor]

Say we have a wave on a string and a function which maps the motion. If one had to assign some type of electric and magnetic field to the wave on a string what would they be?

Could it be that the magnetic field goes as the velocity of a point on the string and the electric field goes as the slope at a point on the string? Both maximum and minimum at the same time?

Thanks for any help!

[Born2bwire]

You wouldn't want to think of in terms of the electromagnetic fields. The electromagnetic fields are vector fields while a wave on a string is a scalar field. There isn't really anything "vector" related to the waves on a string. The parts of the string oscillate in place and so there is no information to be gleaned by their direction. What kind of information do you want to display with a vector wave field?

[Dadface]

I think spinnor just wants an analogy of the electromagnetic field.The best I can think of is the velocity at each point compared to the displacement at those points.

[K^2]

Position and velocity on a vibrating string are out of phase. E and B fields have the same phase. For a linearly polarized plane wave, the E field oscillates perpendicular to the B field, so there isn't really a good analogy here.

[Dadface]

How good does the analogy need to be? How about velocity and tension in string? If tension is a vector it is at 90 to the velocity vector(at max displacement at least)

[K^2]

Under small oscillations, required fore linearity, tension is uniform throughout the string.

[sweet springs]

Hi, Spinnor
Say Ax and Ay be rectangular amplitudes of vibration of string extended to z direction. You can make 45 degree mixed wave so that Ax=Ay and regard them to E and B.
Regards.

[Dadface]

Hello K^2.It's a reasonable assumption to make for small amplitudes but it's still an approximation.If memory serves me correctly for a standing transverse wave in a string the displacement nodes are tension antinodes and vice versa.

[K^2]

That is obviously correct. My point was that a wave deviating sufficiently from the small-oscillation assumption to make this viable will no longer be linear, and will not properly represent an EM wave.

And that probably should have been my last complaint, followed by the fact that phases still don't match and that the vector direction is completely wrong.

[Dadface]

Spinnor referred to a "wave on a string" and not one of small oscillation and of course such a wave,even one with small oscillation, cannot properly represent an EM wave.The analogies presented here have severe shortcomings so are there any better?

[K^2]

And vibrating string isn't a "wave on a string"?

Trying to use a string as an analogy for both E and B fields at the same time is a very silly idea, yes. That's the whole point.

[Spinnor]

You wouldn't want to think of in terms of the electromagnetic fields. The electromagnetic fields are vector fields while a wave on a string is a scalar field. There isn't really anything "vector" related to the waves on a string.

So say we have a wave on a long string (small amplitude so T remains constant) With endpoints fixed in space. Now the string can vibrate in two dimensions (three dimensions if you include longitudnal waves), vectors could be used. Even in the one-dimensional case I think one can think in terms of a one dimensional vector quantity for the displacement of the string.


QUOTE The parts of the string oscillate in place and so there is no information to be gleaned by their direction. [/QUOTE]

If it moves up one unit that can be represented with a vector?

[/QUOTE] What kind of information do you want to display with a vector wave field?[/QUOTE]

Not sure what your asking?

[Spinnor]

I think spinnor just wants an analogy of the electromagnetic field.The best I can think of is the velocity at each point compared to the displacement at those points.


What two things about a wave at some point are proportional to each other and in phase? Transverse velocity at a point and slope at a point is one pair. I don't know if there are others?

[Spinnor]

How good does the analogy need to be? How about velocity and tension in string? If tension is a vector it is at 90 to the velocity vector(at max displacement at least)

For small displacements the tension is assumed constant?

[Spinnor]

Spinnor referred to a "wave on a string" and not one of small oscillation and of course such a wave,even one with small oscillation, cannot properly represent an EM wave.The analogies presented here have severe shortcomings so are there any better?

Small displacements are a must.

[Spinnor]

One can even bring charge into this problem but in this case likes attract. For a string that vibrates in one plane only displace the string a small amount with your finger, that is like charge. If a second finger pushes down on the string both fingers are "attracted" to each other, assume zero friction. If the second finger pushes down very lightly with a force F (a test "charge") the force of attraction has magnitude (F*slope) and points towards the charge.

But nature is way more cool.

Thanks for your replies!

[Spinnor]

One can even bring charge into this problem but in this case likes attract. For a string that vibrates in one plane only displace the string a small amount with your finger, that is like charge. If a second finger pushes down on the string both fingers are "attracted" to each other, assume zero friction. If the second finger pushes down very lightly with a force F (a test "charge") the force of attraction has magnitude (F*slope) and points towards the charge.

But nature is way more cool.

Thanks for your replies!

Now jiggle your finger you get waves on the string and passing waves on the string makes your finger wiggle.

[Spinnor]

If one looks at the Lagrangian for a string one gets the obvious kinetic term and a potential energy term proportional to the slope of the string squared, see

http://www.physics.sfsu.edu/~lea/courses/grad/fldlagr.PDF

equation 1

[Spinnor]

If a finger pushes down on a string and then moves to the right the finger produces a "magnetic" field given by the small transverse velocity of string elements as the finger moves. No movement the "charge" produces no "magnetic" field. Please leave relativity out, the analogy falls on its face.