🚀 go-pugleaf

In article <345D809D.74517784@nlc.net.au>, Lord Shaman
<shaman@nlc.net.au> writes
>    I'm a first year physics student at the university of new south
>wales, and I'm looking for the equation for the simulation of linear
>waves in 2D. I'd like to simulate effects like diffraction,
>interference, reflection and refraction from first principles. I'd like
>to be able to create a "digital ripple tank" in which I can do
>experiments. I need to be able to create barriers, alter the wave speed
>in specific areas and create a source. I've so far had little luck,
>because I can't seem to get my hands on the equation that I need to
>apply to each pixel to get to the next frame in the simulation. I've
>successfully implemented heat diffusion, but that's not what I'm looking
>for. I've tried the university library, but most of the books are either
>on very advanced and unrelated topics like nonlinear waves in quantum
>mechanics, or don't give enough detail to write a program. Please reply
>by email, as my news server is not too good. Any help would be
>appreciated.
>
The general form of the Wave Equation will be in any Maths or Physics
text book. It is

        Del^2(Phi) = (k1)^2 d2(Phi)/dt^2 + k2 d(Phi)/dt + g(x,y,t)

where all derivatives are partial. Phi is the amplitude, usually
pressure in Acoustics or the Electric or Magnetic field strength vector
in Optics. k1 is 1/wave speed. the k2 term is damping, usually small for
acoustics and optics. g is a source term. One method of solution is by
separation of variables, giving time and space functions, with the
constants determined by fitting boundary conditions.

If you want to do a point by point Finite Difference solution then you
may be OK for Acoustics, but the Boundary Conditions are often difficult
to specify. If you want to do optics then the small wavelength is the
problem, typically 500 nm for green or 5x10^-7 m, If you want to resolve
a wavelength, with say 10 points in it, you need a point spacing of
5x10^-8 m. For a 100 mm square area this means 2x10^6 points each way or
4x10^12 points altogether. Not very practical. In the real world,
Reflection, diffraction, lens design, holography, image modification
etc. are all done by Fourier Transform optics, which is a completely
different approach.

Have I answered the right question?


-- 
David Wilkinson