# Time averaged intensity, derivation and vector plot

1. Sep 27, 2015

### snickersnee

1. The problem statement, all variables and given/known data
I'm trying to graph this equation:

I'm trying to use the champ command in scilab to graph this from -π to π on the kx and ky axes.
But this requires the x and y components of the vector as arguments. How do I get those components, is there a command for that? There's also the quiver command in matlab but that also requires components. I have scilab so that would help more, but you can use matlab if you really want to.

I'm also trying to figure out how to get that equation from this one and this one
Any pointers in that area would be much appreciated.

2. Relevant equations
See above

3. The attempt at a solution

For the derivation, I don't really know but this might be helpful:
Also it might use euler's identity, the one that relates complex exponential as cos + j*sin.

This is how the graph is supposed to look.

The following scilab code doesn't work:

po=1;
rho= 1.21 //kg/m^3
c=343 //m/s

I=po^2/(2*rho*c);
kx=-%pi:%pi;
ky=-%pi:%pi;
Ix=-sin(kx).*cos(ky);
Iy=cos(kx).*sin(ky);
champ(kx, ky, I.*Ix, I.*Iy )

Last edited: Sep 27, 2015
2. Oct 2, 2015