{VERSION 4 0 "IBM INTEL NT" "4.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 } {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Text Output" -1 2 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 0 0 0 0 0 1 3 0 3 1 } 1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Warning" 2 7 1 {CSTYLE "" -1 -1 "" 0 1 0 0 255 1 0 0 0 0 0 0 1 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Output" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple P lot" 0 13 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "R3 Font 0" -1 256 1 {CSTYLE "" -1 -1 "Helvetica" 1 10 0 0 255 1 2 1 2 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "R3 Font 2" -1 257 1 {CSTYLE "" -1 -1 "Couri er" 1 10 0 0 0 1 2 1 2 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 91 "c International Thomson Pu blishing Bonn 1995 filename: wellen2.ms" }} {PARA 0 "" 0 "" {TEXT -1 104 "Autor: Komma \+ Datum: 20.10.93" }} {PARA 0 "" 0 "" {TEXT -1 61 "Thema: transversale Wellen, longitudinale Wellen, Kreiswellen" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 " " {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 103 "Wellen im Medium (eindimensional). Motto: \"Wie begegen sich die Teilchen -- wie beweg t sich die Phase?\"" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 " " {TEXT -1 21 "1. Transversale Welle" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "restart:with(plots):" }}{PARA 7 "" 1 "" {TEXT -1 50 " Warning, the name changecoords has been redefined\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "#n:=20:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 73 "#pl:=plot([seq([i,1+cos(2*Pi/n*(i))],i=1..n)],style=p oint,color=red): pl;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "n:= 20:t:='t':" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 86 "ps:=seq(plot( \{[seq([i,1+(cos(2*Pi/n*(i+t)))],i=1..n)]\},color=red,style=point),t=1 ..n):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "display([ps],inseq uence=true); " }}{PARA 13 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 71 "Richtu ngswechsel im Plotfenster m\366glich, also ohne \"Programmierarbeit\". " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 14 "stehende Welle" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "t:='t':" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 106 "ps:=seq(plot(\{[seq([i,1+(cos(2*Pi/n*(i+t)))+(cos(2*Pi/n*(i-t)))] ,i=1..n)]\},color=red,style=point),t=1..n):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "display([ps],insequence=true); " }{TEXT -1 0 "" }} {PARA 13 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 23 "2. Longitudinale Welle:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "#ar:=array(1..n);t:=0;" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "loop:=proc() global ar;" } }{PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "for i to n do" }}{PARA 0 "> " 0 " " {MPLTEXT 1 0 26 "ar[i]:=i+sin(2*Pi/n*(i+t))" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "od:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "end;" }} {PARA 7 "" 1 "" {TEXT -1 62 "Warning, `i` is implicitly declared local to procedure `loop`\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%loopGR6\" 6#%\"iGF&F&?(8$\"\"\"F+%\"nG%%trueG>&%#arG6#F*,&F*F+-%$sinG6#,$*&*&%#P iGF+,&F*F+%\"tGF+F+F+F,!\"\"\"\"#F+F&6#F0F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "n:=20: t:='t': loop():" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 68 "ps:=seq(plot([seq([ar[i],1],i=1..n)],style=point,co lor=red),t=1..n):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "displa y([ps],insequence=true);" }}{PARA 13 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 15 "stehende Welle:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "loop:=p roc() global ar;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "for i to n do" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "ar[i]:=i+sin(2*Pi/n*(i+t))+sin(2* Pi/n*(i-t))" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "od:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "end;" }}{PARA 7 "" 1 "" {TEXT -1 62 "Warning, `i` is implicitly declared local to procedure `loop`\n" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#>%%loopGR6\"6#%\"iGF&F&?(8$\"\"\"F+%\"nG%%trueG>&%#ar G6#F*,(F*F+-%$sinG6#,$*&*&%#PiGF+,&F*F+%\"tGF+F+F+F,!\"\"\"\"#F+-F46#, $*&*&F9F+,&F*F+F;F " 0 "" {MPLTEXT 1 0 21 "#loop(); ein testplot" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 57 "#pl:=plot([seq([ar[i],1],i=1..n)],style=point,color=r ed):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "#pl;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "t:='t':loop():" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 68 "ps:=seq(plot([seq([ar[i],1],i=1..n)],style=p oint,color=red),t=1..n):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "display([ps],insequence=true);" }}{PARA 13 "" 1 "" {TEXT -1 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 18 "3. \"Wasserwellen\":" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "restart:with(plots):" }}{PARA 7 "" 1 "" {TEXT -1 50 " Warning, the name changecoords has been redefined\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "n:=20:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "loop:=proc() global ar;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "for i to n do" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "a r[i]:=i+sin(2*Pi/n*(i+t))" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "od:" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "end;" }}{PARA 7 "" 1 "" {TEXT -1 62 "Warning, `i` is implicitly declared local to procedure `loop`\n" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%%loopGR6\"6#%\"iGF&F&?(8$\"\"\"F+%\" nG%%trueG>&%#arG6#F*,&F*F+-%$sinG6#,$*&*&%#PiGF+,&F*F+%\"tGF+F+F+F,!\" \"\"\"#F+F&6#F0F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "t:='t' ;loop():" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"tGF$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 90 "ps:=seq(plot(\{[seq([ar[i],1+(cos(2*Pi/n* (i+t)))],i=1..n)]\},color=red,style=point),t=1..n):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 81 "display([ps],insequence=true); ######### ##### constrained ! ###################" }}{PARA 13 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 " " 0 "" {TEXT -1 30 "Wie bewegen sich die Teilchen?" }}{PARA 0 "" 0 "" {TEXT -1 68 "Zur \"optischen Unterst\374tzung\" kann ein \"Kreis\" mit eingebaut werden:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "x:='x ':y:='y':" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 74 "kreis:=implici tplot((x-10)^2+(y-1)^2=1,x=9..11,y=0..2,numpoints=5):#kreis;" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "n:=20;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"nG\"#?" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 105 "ps:=seq(display(\{kre is,plot([seq([ar[i],1+(cos(2*Pi/n*(i+t)))],i=1..n)])\},color=red,style =point),t=1..n):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 51 "display([ps],insequence=true,scaling=constrained); \+ " }}{PARA 13 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 60 "So bewegen sich die Teilchen! Und wie bewegt sich die Welle?" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 56 "Kann man f\374r die Koordinaten beliebige Funktion nehmen? " }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "restart:with(plots):" }} {PARA 7 "" 1 "" {TEXT -1 50 "Warning, the name changecoords has been r edefined\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "n:=20:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "t:='t':" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "f:=(i,t)->(i-t)^2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fGR6$%\"iG%\"tG6\"6$%)operatorG%&arrowGF)*$),&9$\" \"\"9%!\"\"\"\"#F1F)F)F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 71 "ps:=seq(plot(\{[seq([i,f(i,t)],i=1..n)]\},color=red,style=point),t=1. .n):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 79 "#ps:=seq(plot(\{[se q([ar[i],1+(cos(2*Pi/n*(i+t)))],i=1..n)]\},color=red),t=1..n):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "display([ps],insequence=true ); " }}{PARA 13 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 320 "Die Verschie bungsgleichung verschiebt nat\374rlich beliebige Funktionen. Aber f \374r eine physikalische Welle sollte wohl doch der Massenpunkt im Mit tel an einem Ort bleiben. Aber man kann auch mit unbeschr\344nkten Fun ktionen eine Bewegung herstellen, die in endlichen Zeitintervallen nic ht von \"der Welle\" zu unterscheiden ist." }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 25 "komma@oe.un i-tuebingen.de" }}}}{MARK "0 2 0" 7 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }