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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 84 "Wave Packet Problem       \+
                                               BMsteer.MWS" }}{PARA 0 
"" 0 "" {TEXT -1 82 "'steering a beam' in Multiple Source Interference
         8/25/95 after BMWidth.ms" }}{PARA 0 "" 0 "" {TEXT -1 84 "Lear
ning objectives: Translation of equation for 2D wave to off-origin sou
rce points" }}{PARA 0 "" 0 "" {TEXT -1 77 "                           \+
         Physical intuition regarding interference" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 89 "Show a radiated beam bein
g 'steered' by changing the phase shift between adjacent sources" }}
{PARA 0 "" 0 "" {TEXT -1 37 "                                     " }}
{PARA 0 "" 0 "" {TEXT -1 16 "MAPLE: animate3d" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 8 "Remarks:" }}{PARA 0 "" 0 "
" {TEXT -1 47 "Takes some minutes to execute on most machines." }}
{PARA 0 "" 0 "" {TEXT -1 65 "Array of sources extends along the x-axis
, centered at the origin" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "
" 0 "" {TEXT -1 48 "Wavelength, spacing, x, and y could be in meters" 
}}{PARA 0 "" 0 "" {TEXT -1 35 "k0 = wave number = 2 Pi/ wavelength" }}
{PARA 0 "" 0 "" {TEXT -1 34 "spacing = distance between sources" }}
{PARA 0 "" 0 "" {TEXT -1 44 "xmax, ymax used to set plot range dimensi
ons" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(plots):" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 16 "wavelength:=1.0;" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 25 "k0:=628/(100*wavelength);" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 13 "NrSources:=4;" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 14 "spacing:=6/10;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 10 "Atotal:=0;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "for j
 from 1 to NrSources" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "     do" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 106 "          m:=(2*j-5)/2:           \+
                    #      m =  \{-3/2 , -1/2, 1/2, 3/2\} for four sou
rces" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 72 "          r:=((x-m*spacing)
^2+y^2)^0.5:  # distance from source to (x,y)" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 41 "          Atotal:=Atotal+cos(k0*r-m*phi):" }}{PARA 0 
"> " 0 "" {MPLTEXT 1 0 9 "      od:" }}}{EXCHG {PARA 2 "" 0 "" {TEXT 
-1 1 "\n" }}{PARA 0 "" 0 "" {TEXT -1 87 "Atotal:=A[1]+A[2]+...+A[NrSou
rces]: #  amplitude pattern at t=0 due to all four sources" }}{PARA 2 
"" 0 "" {TEXT -1 1 "\n" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 57 "### Animate the effect of ch
anging source separations ###" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 38 "xmax:=4: ymax:=4: #Set plot area scale" }}}{EXCHG {PARA 0 "" 0 "
" {TEXT -1 98 "The orientation is theta=0, phi =0 (phi = any), so the \+
x-axis goes down as we look from the z-axis" }}{PARA 2 "" 0 "" {TEXT 
-1 1 "\n" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 195 " animate3d(Atotal, x=-
xmax..xmax, y=-ymax/5..9*ymax/5,phi=0/10..14/10, grid=[35,35],style=pa
tchnogrid, shading=zgreyscale, scaling=constrained, orientation=[0,Pi/
4], tickmarks=[0,0,0],frames=10);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}
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