{VERSION 2 3 "IBM INTEL NT" "2.3" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 } {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 0 0 0 0 0 0 }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 0 }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 }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 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 11 12 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }1 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 12 255 0 0 1 2 1 2 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 } {PSTYLE "R3 Font 2" -1 257 1 {CSTYLE "" -1 -1 "Courier" 1 12 0 0 0 1 2 2 2 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 80 "PHYSICS RESOURCE PACKETS P ROJECT File: FUZZYTV.MWS" }}{PARA 0 "" 0 "" {TEXT -1 110 "Rose-Hulman Institute of Technology \+ Authors: Perry Peters & Greg Williby" }}{PARA 0 "" 0 "" {TEXT -1 97 "http://www.rose-hulman.edu/~moloney \+ Software: Maple V Release 4" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 774 "TV sets receiving signal s out of the air without benefit of cable are sometimes subject to per iodic jumping of the picture when an airplane flies through or near th e line-of-sight to the TV station. The line of sight distance from st ation to the TV set is 10 miles, and the wavelength is 9.5 feet. The \+ TV station is at the origin (0,0,0) and the TV set is at (10,0,0) mi. \+ An airplane flies perpendicular to this line at an altitude of 1/2 mi le at a speed of 150 mi/hr. At t=0, the plane is closest to the TV se t. At that time, its coordinates are (9.0, 0, 0.5) mi. Find the firs t 3 times after t=0 when waves bouncing off the plane will be out of p hase with waves arriving directly at the set from the station. (At th is point, the TV picture should be all messed up.)" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "with(linalg):" }}{PARA 7 "" 1 "" {TEXT -1 32 "Warning, new definition for norm" }}{PARA 7 "" 1 "" {TEXT -1 33 "Warning, new definition for trace" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 14 "with(student):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "assume(t>0);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 51 " The location of the plane in miles. t is in hours." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "plane:=vector([9,150*t,1/2]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&planeG-%'VECTORG6#7%\"\"*,$%#t|irG\"$]\"#\"\"\"\"\"# " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 38 "The location of the TV statio n (miles)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "station:=vector([0,0,0 ]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%(stationG-%'VECTORG6#7%\"\"!F )F)" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 34 "The location of the TV set (miles)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "TVset:=vector([10,0,0]) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&TVsetG-%'VECTORG6#7%\"#5\"\"!F *" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 39 "Distance from the station to the plane." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "dist1:=distance(stat ion,plane);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&dist1G,$*$,&\"#8\"\" \"*$%#t|irG\"\"#\"%+O#F)F,#\"\"&F," }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 38 "Distance from the plane to the TV set." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "dist2:=distance(TVset,plane);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&dist2G,$*$,&\"\"&\"\"\"*$%#t|irG\"\"#\"&++*#F)F,F." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 35 "Total path length of reflected \+ wave" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "distreflect:=dist1+dist2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%,distreflectG,&*$,&\"#8\"\"\"*$%#t |irG\"\"#\"%+O#F)F,#\"\"&F,*$,&F0F)F*\"&++*F.F." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 42 "Distance from the TV station to the TV set" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "distdirect:=10;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%+distdirectG\"#5" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 62 "Path difference between the direct path and the reflected path" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "difference:=distreflect-distdirect; " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%+differenceG,(*$,&\"#8\"\"\"*$%# t|irG\"\"#\"%+O#F)F,#\"\"&F,*$,&F0F)F*\"&++*F.F.!#5F)" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 231 "Since a phase shift of 180 deg occurs wh en the waves are reflected from the plane, distructive interference wi ll occur when the path difference is a multiple of 9.5 feet. Convert \+ 9.5 feet into miles to solve the equation for time." }}{PARA 0 "" 0 " " {TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "sol:=solve(differ ence=n*(95/10)/5280,t);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%$solG6$,$ *&,,!4+++'\\)HGNC\"\"\"\"%\"nG\"2++!G4i=m:*$F+\"\"#\"/+g!\"\"#F*\"(+!oJ,$F'#F:F< " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 33 "Pick the positive value for t ime." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "Time:=sol[1];" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#>%%TimeG,$*&,,!4+++'\\)HGNC\"\"\"\"%\"nG\"2++!G4 i=m:*$F*\"\"#\"/+g!\"\"#F)\"(+!oJ" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 39 "Find th e path difference in feet at t=0" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "dist0:=evalf(subs(t=0,difference))*5280;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&dist0G$\"+/J'\\'p!\"(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 27 "Find the value of n at t=0." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "dist0/9.5;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+5,a Jt!\")" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 55 "Distructive interferenc e would first occur when n = 74." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 115 "Find the first three times in seconds wh en the reflected signal is 180 degrees out of phase with the direct si gnal." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "for n from 74 to 76 do" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "time.(n-73)=evalf(Time*3600);" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "od;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%&time1G$\"+k!*G)=\"!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%&tim e2G$\"+9-ik=!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%&time3G$\"+7dhaB !\"*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 57 "The 'fuzzy' signals are o ccurring every 0.7 seconds or so" }}}}{MARK "17 0 0" 3 }{VIEWOPTS 1 1 0 1 1 1803 }