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{SECT 0 {EXCHG {PARA 206 "" 0 "" {TEXT 206 88 "PH424 1-D Waves, Oregon
 State University, Department of Physics.   Janet Tate, 1997-2009" }
{TEXT 206 0 "" }}{PARA 206 "" 0 "" {TEXT 206 45 "BASIC CONCEPTS IN WAV
ES:  \"MATERIAL\" VELOCITY" }{TEXT 206 0 "" }{TEXT 206 215 "\nThe name
 \"material velocity\" is not a very good one, and has meaning only wh
en the wave propagates in a material like string or air.  It then refe
rs to the velocity of the  particles that support the disturbance.  " 
}{TEXT 206 0 "" }}}{EXCHG {PARA 207 "> " 0 "" {MPLTEXT 1 0 20 "restart
:with(plots):" }{MPLTEXT 1 0 0 "" }}{PARA 208 "" 1 "" {TEXT 208 49 "Wa
rning, the name changecoords has been redefined" }{TEXT 208 0 "" }}}
{EXCHG {PARA 206 "" 0 "" {TEXT 206 124 "Let's start with a waveform (s
ay a transverse wave on a string) that has wavelength 1 m, period 1 s,
 amplitude 0.1 m (10cm)." }{TEXT 206 0 "" }}}{EXCHG {PARA 207 "> " 0 "
" {MPLTEXT 1 0 33 "f:=(x,t)->0.1*cos(2*Pi*x-2*Pi*t);" }{MPLTEXT 1 0 0 
"" }}{PARA 209 "" 1 "" {XPPMATH 20 "6#>I\"fG6\"f*6$I\"xGF%I\"tGF%F%6$I
)operatorGF%I&arrowGF%F%*&$\"\"\"!\"\"F/-I$cosGF%6#,&*&I#PiGI*protecte
dGF7F/9$F/\"\"#*&F6F/9%F/!\"#F/F%F%F%" }{TEXT 20 0 "" }}}{EXCHG {PARA 
207 "> " 0 "" {MPLTEXT 1 0 7 "f(x,t);" }{MPLTEXT 1 0 0 "" }}{PARA 209 
"" 1 "" {XPPMATH 20 "6#,$-I$cosG6$I*protectedGF'I(_syslibG6\"6#,&*&I#P
iGF'\"\"\"I\"xGF)F.\"\"#*&F-F.I\"tGF)F.!\"#$F.!\"\"" }{TEXT 20 0 "" }}
}{EXCHG {PARA 206 "" 0 "" {TEXT 206 64 "Now we isolate the displacemen
t of our string  at the position :" }{TEXT 206 0 "" }}}{EXCHG {PARA 
207 "> " 0 "" {MPLTEXT 1 0 23 "g:=t->0.1*cos(-2*Pi*t);" }{MPLTEXT 1 0 
0 "" }}{PARA 209 "" 1 "" {XPPMATH 20 "6#>I\"gG6\"f*6#I\"tGF%F%6$I)oper
atorGF%I&arrowGF%F%*&$\"\"\"!\"\"F.-I$cosG6$I*protectedGF3I(_syslibGF%
6#,$*&I#PiGF3F.9$F.!\"#F.F%F%F%" }{TEXT 20 0 "" }}}{EXCHG {PARA 206 ""
 0 "" {TEXT 206 238 "We'll look at these functions over a distance cor
responding to a little over one wavelength and a time of 2 periods.  \+
\"a1\"  represents the string, which is red.  \"a2\" represents a smal
l portion of the string near x=0 -- it's painted blue." }{TEXT 206 0 "
" }}}{EXCHG {PARA 207 "> " 0 "" {MPLTEXT 1 0 60 "a1:=animate(f(x,t),x=
-0.6..0.6,t=0..2,colour=red,frames=30):" }{MPLTEXT 1 0 0 "" }}}{EXCHG 
{PARA 207 "> " 0 "" {MPLTEXT 1 0 86 "a2:=animate(g(t),x=-.01..0.01,t=0
..2,colour=blue,style=point,symbol=circle,frames=30):" }{MPLTEXT 1 0 
0 "" }}}{EXCHG {PARA 206 "" 0 "" {TEXT 206 87 "After you execute the \+
\"display\" command and see the resulting graph, animate the graph." }
{TEXT 206 0 "" }}}{EXCHG {PARA 207 "> " 0 "" {MPLTEXT 1 0 15 "display(
a1,a2);" }{MPLTEXT 1 0 0 "" }}{PARA 210 "" 1 "" {GLPLOT2D 400 400 400 
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1.0 45.0 45.0 1 0 "Curve 1" "Curve 2" }}{TEXT 209 0 "" }}}{EXCHG 
{PARA 207 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 206 "" 0 "" 
{TEXT 206 190 "1.  Pick any particular feature like a crest or a troug
h or a zero.  How far does the feature move in the horizontal directio
n in, say, 1 s?  What is the feature's velocity in meters/second?" }
{TEXT 206 0 "" }}{PARA 206 "" 0 "" {TEXT 206 319 "2.  Concentrate on t
he blue portion of the string.  How far does the blue piece of string \+
move in, say, 1 s?  What is the velocity of the blue portion of the st
ring in meters/second?  (You may wish to get a more realistic picture \+
by choosing the \"constrained\" feature for the axes -- this scales bo
th axes the same way." }{TEXT 206 0 "" }}{PARA 206 "" 0 "" {TEXT 206 
79 "3.  Does the blue portion of the string move in the horizonal dire
ction at all?" }{TEXT 206 0 "" }}{PARA 206 "" 0 "" {TEXT 206 260 "4.  \+
Is the difference between the \"phase velocity\" (or feature velocity)
 in the horizontal direction   and the \"string velocity\" or \"materi
al velocity\" or \"transverse velocity\" (the velocity of any part of \+
the string)  clear to you?  If not, ask an instructor." }{TEXT 206 0 "
" }}}{EXCHG {PARA 206 "" 0 "" {TEXT 206 16 "END OF WORKSHEET" }{TEXT 
206 0 "" }}}{PARA 211 "" 0 "" {TEXT 203 0 "" }}{PARA 212 "" 0 "" 
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