Wave Equation: U is Amplitude Vector?

[PhiJ]

In the wave equation, what is u, is it the amplitude?
If it is, how can it be a vector?

 

[inha]

With that description it's impossible to tell. Post the whole equation.

 

[mezarashi]

If you're referring to D'Alembert's wave equation, then yes, and I assume:

$$\bigtriangledown^2 u = \frac{1}{c^2} \frac{\delta^2 u}{\delta t^2}}$$

 

[marlon]

In the wave equation, what is u, is it the amplitude?

YES

If it is, how can it be a vector?

Why couldn't it be ?

Do you know the concept of a phasor ?

I suggest you look for the mathematical formalism behind wave-dynamics.
Try the Hyperphysics website.

marlon

 

[PhiJ]

Yup, that's what I meant by the wave equation.

I'm a bit confused as to what I am meant to put on what forum area, as the question got moved, but it definitely wasn't a schoolwork question, as it is beyond that, and it wasn't a coursework or textbook question either. Am I meant to just post every question that is to help me learn physics on this section, or what?

Haven't heard of a phasor. By the hyperphysics website, do you mean hyperphysics.phy-astr.gsu.edu?

 

[mezarashi]

A phasor is essentially a vector in an Im-Re plane. It's not easy to grasp the concept right off, so I suggest reading related material.

 

[marlon]

Haven't heard of a phasor. By the hyperphysics website, do you mean hyperphysics.phy-astr.gsu.edu?

A phasor is just a rotating vector (angle : wt), expressed in a XY-plane, of which the y component expresses the amplitude of a harmonic oscillation.

http://hyperphysics.phy-astr.gsu.edu/hbase/electric/phase.html


marlon

 

[PhiJ]

I understand why phase is reperesented as an angle, as your graph is a sin curve, but why do you represent it as an angle on the complex plane? Is it because you then have the angle between when the formula for the point is i sin theta and cos theta?

I thought amplitude was not a vector because then you could say that two waves have the same amplitude even if they are oscilating on different planes. Obviously not.

 

[mathphys]

in the wave equation U can be an scalar field or a vector field.

The Laplacian is defined for both of them. In the vectorial case you have a vectorial amplitude, and two waves will have the same amplitude if their vectorial amplitudes are equal.

 

[PhiJ]

u is a field!? I thought it was an amplitude!

 

[mathphys]

As a funtion of both the coordinates and the time U=U(r,t) is a field. Depending if it is a scalar or a vectorial function it represents the corresponding kind of field.


Physically that field may represent oscillations, which have 'amplitude' and' phase'. For instance U may represent the electric field (a vectorial field) of a propagating electromagnetic wave.

 

[PhiJ]

U is a field! Does that mean that U(r,t) is the function, that, if you input your position, time, and other important things (e.g. charge) then it will give you the force you experience? How would this work for a photon though?

 

[mathphys]

Well, i actually meaned a field in these sense
http://en.wikipedia.org/wiki/Scalar_field
and this other one
http://en.wikipedia.org/wiki/Vector_field
What function U represents physically depends on the context, many phenomena may be described by the wave equation.:
http://en.wikipedia.org/wiki/Wave_equation
and this is an example of such phenomena
http://en.wikipedia.org/wiki/Electromagnetic_wave_equation
About your other statemets/questions, well, let's say that they were 'too appresurate'.

 

[PhiJ]

So to solve, you would need $$\frac{\partial^2 u}{\partial x^2}$$ in terms of t?