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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 91 "beats.mws  modified from d
eepsea1.  18 Aug 95  . phase velocity equals the group velocity. " }}
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0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 12 "with(plots):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 35 "c:=2;  # phase velocity of the wave" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 112 "write down the dispersion relation;  this medium is not \+
dispersive, and the phase and group velocities are equal" }}{PARA 0 ">
 " 0 "" {MPLTEXT 1 0 11 "omega:=c*k;" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 23 "psi:=sin(k*x-omega*t); " }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 21 "y[1]:=subs(k=k1,psi);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 21 "y[2]:=subs(k=k2,psi);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "vp:=ome
ga/k;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "vg:=diff(omega,k);
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "ratio:=vp/vg; # phase v
elocity over group velocity" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
32 "evalf(subs(k=10,g=98/10,ratio));" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 19 "y_total:=y[1]+y[2];" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 24 "values:=\{k1=5,k2=45/10\};" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 24 "m:=subs(values,y_total);" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 17 "NN:=25; dtime:=6;" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 67 "h:=animate(m,x=-2..8,t=0..dtime,frames=NN,color=red,n
umpoints=150):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 91 "g:=animat
e(subs(values,y[1]),      x=-2..8,t=0..dtime,color=black,frames=NN,num
points=150):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 94 " i:=animate
(subs(values,y[2]),       x=-2..8,t=0..dtime,color=blue,  frames=NN,nu
mpoints=150):" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 69 "g:=animate(f[2],
x=0..20,t=0..30,color=green,frames=15,numpoints=100):" }}{PARA 0 "" 0 
"" {TEXT -1 65 "i:=animate(m,x=0..20,t=0..30,color=blue,frames=15,nump
oints=100):" }}{PARA 0 "" 0 "" {TEXT -1 14 "j:=display(h):" }}{PARA 2 
"" 0 "" {TEXT -1 1 "\n" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "j:=displa
y([h,g]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "display([i,j])
;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 79 "In this animation, we imagin
e ourselves at x=0 with the 'beats' moving past us." }}{PARA 2 "" 0 "
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