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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 21 "Stantrav.mws  7/25/95" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 79 "For all p
arts of this problem, use a wavelength of 1 m and a frequency of 1 Hz.
" }}{PARA 0 "" 0 "" {TEXT -1 178 "a) Create an animation of a wave tra
veling to the right. Show at least one cycle of the motion.  b) Repeat
 part a) for a wave traveling to the left, same amplitude as in part a
)." }}{PARA 0 "" 0 "" {TEXT -1 84 "c) Repeat part a), adding together \+
the traveling waves to the left and to the right." }}{PARA 0 "" 0 "" 
{TEXT -1 78 "d) Repeat part c), but have the amplitudes of the two tra
veling waves unequal." }}{PARA 0 "" 0 "" {TEXT -1 83 "e) Write down th
e equation of a standing wave. Animate this for one or more cycles." }
}{PARA 0 "" 0 "" {TEXT -1 74 "Paste in the plots at the end of each an
imation on the sheet you turn in. " }}{PARA 0 "" 0 "" {TEXT -1 56 "Ind
icate on the plot what happened during the animation." }}{PARA 0 "" 0 
"" {TEXT -1 95 "optional: f) put the two traveling waves (equal amplit
udes) and their sum on the same animation" }}{PARA 0 "" 0 "" {TEXT -1 
0 "" }}{PARA 0 "" 0 "" {TEXT -1 44 "Here is a sample animate command t
o try out." }}{PARA 0 "" 0 "" {TEXT -1 68 "animate(t*cos(x),x=-3..3,t=
0..1,frames=20,numpoints=50,color=blue); " }}{PARA 2 "" 0 "" {TEXT -1 
1 "\n" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 
0 "" 0 "" {TEXT -1 41 "wavelength is 1 meter; frequency is 1 hz;" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "k:=2
*Pi; " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "Omega:=2*Pi;" }}}
{EXCHG {PARA 2 "" 0 "" {TEXT -1 1 "\n" }}{PARA 0 "> " 0 "" {MPLTEXT 1 
0 42 "sr:=sin(k*x-Omega*t); # going to the right" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 41 "sl:=sin(k*x+Omega*t); # going to the left" }}
}{EXCHG {PARA 2 "" 0 "" {TEXT -1 1 "\n" }}{PARA 0 "> " 0 "" {MPLTEXT 
1 0 12 "with(plots):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 82 "ani
mate(sr,x=0..2,t=0..1,frames=20,numpoints=200);  #  traveling wave to \+
the right" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 81 "animate(sl,x=0
..2,t=0..1,frames=20,numpoints=200);   # traveling wave to the left" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 85 "animate(\{sl,sr\},x=0..2,t
=0..1,frames=20,numpoints=200,color=green); # both trav waves" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 87 "animate(sl+sr,x=0..2,t=0..1,
frames=20,numpoints=200,color=blue);  # add the trav waves " }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "w:=sin(k*x)*cos(Omega*t);" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "animate(w,x=0..2,t=0..1,fr
ames=20,numpoints=200,color=black);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 
-1 65 "If you animate several functions at once, you get only one colo
r." }}{PARA 0 "" 0 "" {TEXT -1 86 "Here is a way to animate several th
ings at once, with separate colors and other stuff." }}{PARA 2 "" 0 "
" {TEXT -1 1 "\n" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "Nframes:=20;   \+
 " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "for i from 0 to Nframe
s-1 do" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "j:=1/(Nframes):" }}{PARA 
0 "> " 0 "" {MPLTEXT 1 0 74 "pr.(i):= plot(subs(t=i*j,sr),x=0..2,numpo
ints=100,color=red,thickness=2): " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 
63 "pl.(i):= plot(subs(t=i*j,sl),x=0..2,numpoints=100,color=blue): " }
}{PARA 0 "> " 0 "" {MPLTEXT 1 0 79 "ps.(i):= plot(subs(t=i*j,sr+sl),x=
0..2,numpoints=100,color=black,thickness=3): " }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 42 "ptot.(i):=display(\{pr.(i),pl.(i),ps.(i)\});" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "od:" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "display
([ptot.(0..Nframes-1)],insequence=true);" }}}{EXCHG {PARA 0 "> " 0 "" 
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