harmonic addition
DESCRIPTION
Spreadsheet used to visually see the addition of various sinusoidal forms through superposition of waves.TRANSCRIPT
83
-2
-1
0
1
2
First 3 Harmonics
Wave 1
Wave 2
wave 3
-2
-1
0
1
2
First 24 Harmonics
Wave 1 Wave 2 wave 3
wave 4 wave 5 wave 6
wave 7 wave 8 wave 9
wave 10 wave 11 wave 12
wave 13 wave 14 wave 15
wave 16 wave 17 wave18
wave 19 wave 20 wave 21
wave 22 wave 23 wave 24
-14
-10
-6
-2
2
6
10
14
First 24 + ResultantWave 1 Wave 2 wave 3
wave 4 wave 5 wave 6
wave 7 wave 8 wave 9
wave 10 wave 11 wave 12
wave 13 wave 14 wave 15
wave 16 wave 17 wave18
wave 19 wave 20 wave 21
wave 22 wave 23 wave 24
sum
-14
-10
-6
-2
2
6
10
14
Resultant
Column AE
0
2
4
6
8
10
12
Chart Title
Column Y
-14
-10
-6
-2
2
6
10
14
First 24 + ResultantWave 1 Wave 2 wave 3
wave 4 wave 5 wave 6
wave 7 wave 8 wave 9
wave 10 wave 11 wave 12
wave 13 wave 14 wave 15
wave 16 wave 17 wave18
wave 19 wave 20 wave 21
wave 22 wave 23 wave 24
sum
-14
-10
-6
-2
2
6
10
14
Resultant
Column AE
0
2
4
6
8
10
12
Chart Title
Column Y
Degree position amplitude absolute value0 187 0 0.000000 15.000000
175 0 0.000000186 0 0.000000188 0 0.000000176 0 0.000000174 0 0.000000185 0 0.000000189 0 0.000000177 0 0.000000173 0 0.000000190 0 0.000000184 0 0.000000172 0 0.000000178 0 0.000000191 0 0.000000171 0 0.000000183 0 0.000000179 0 0.000000192 0 0.000000170 0 0.000000182 0 0.000000180 0 0.000000193 0 0.000000169 0 0.000000164 0 0.000000165 0 0.000000198 0 0.000000197 0 0.000000163 0 0.000000205 0 0.000000206 0 0.000000199 0 0.000000157 0 0.000000156 0 0.000000166 0 0.000000204 0 0.000000207 0 0.000000196 0 0.000000158 0 0.000000155 0 0.000000162 0 0.000000203 0 0.000000208 0 0.000000194 0 0.000000
221 0 0.000000222 0 0.000000200 0 0.000000149 0 0.000000220 0 0.000000148 0 0.000000159 0 0.000000154 0 0.000000141 0 0.000000168 0 0.000000223 0 0.000000140 0 0.000000150 0 0.000000213 0 0.000000142 0 0.000000147 0 0.000000214 0 0.000000237 0 0.000000238 0 0.000000219 0 0.000000236 0 0.000000139 0 0.000000133 0 0.000000132 0 0.000000212 0 0.000000239 0 0.000000224 0 0.000000253 0 0.000000125 0 0.000000209 0 0.000000215 0 0.000000134 0 0.000000254 0 0.000000124 0 0.000000252 0 0.000000167 0 0.000000235 0 0.000000143 0 0.000000126 0 0.000000117 0 0.000000131 0 0.000000269 0 0.000000151 0 0.000000116 0 0.000000229 0 0.000000
255 0 0.000000270 0 0.000000146 0 0.000000268 0 0.000000230 0 0.000000118 0 0.000000109 0 0.000000202 0 0.000000123 0 0.000000251 0 0.000000101 0 0.000000161 0 0.000000138 0 0.000000285 0 0.000000240 0 0.000000108 0 0.000000100 0 0.000000286 0 0.000000228 0 0.000000110 0 0.000000153 0 0.000000284 0 0.000000218 0 0.000000271 0 0.000000135 0 0.000000102 0 0.000000115 0 0.000000
85 0 0.000000301 0 0.000000127 0 0.000000267 0 0.000000
93 0 0.000000195 0 0.000000245 0 0.000000
84 0 0.000000302 0 0.000000300 0 0.000000
86 0 0.00000092 0 0.00000069 0 0.000000
317 0 0.000000231 0 0.000000246 0 0.000000287 0 0.000000
94 0 0.000000
256 0 0.000000119 0 0.000000107 0 0.000000234 0 0.000000
99 0 0.000000283 0 0.000000
68 0 0.00000077 0 0.000000
318 0 0.000000211 0 0.000000316 0 0.000000
53 0 0.00000070 0 0.000000
225 0 0.000000333 0 0.000000244 0 0.000000130 0 0.000000
76 0 0.000000261 0 0.000000
52 0 0.00000037 0 0.000000
216 0 0.000000111 0 0.000000303 0 0.000000103 0 0.000000
61 0 0.00000054 0 0.00000078 0 0.000000
332 0 0.000000334 0 0.000000299 0 0.000000
83 0 0.000000349 0 0.000000
21 0 0.000000250 0 0.000000262 0 0.000000
36 0 0.00000045 0 0.000000
272 0 0.00000038 0 0.00000060 0 0.000000
122 0 0.000000160 0 0.000000
5 0 0.00000091 0 0.000000
29 0 0.00000013 0 0.00000062 0 0.000000
348 0 0.000000357 0 0.000000
87 0 0.000000350 0 0.000000277 0 0.000000
20 0 0.00000022 0 0.000000
319 0 0.000000201 0 0.000000260 0 0.000000
67 0 0.00000044 0 0.000000
315 0 0.00000046 0 0.000000
6 0 0.0000004 0 0.000000
341 0 0.00000028 0 0.00000012 0 0.000000
358 0 0.000000293 0 0.000000
14 0 0.00000030 0 0.00000095 0 0.000000
356 0 0.000000247 0 0.000000
71 0 0.000000278 0 0.000000266 0 0.000000325 0 0.000000309 0 0.000000114 0 0.000000
51 0 0.000000342 0 0.000000
75 0 0.000000227 0 0.000000144 0 0.000000288 0 0.000000331 0 0.000000335 0 0.000000276 0 0.000000340 0 0.000000
294 0 0.00000055 0 0.000000
326 0 0.000000310 0 0.000000324 0 0.000000241 0 0.000000
35 0 0.000000292 0 0.000000
79 0 0.000000308 0 0.000000
39 0 0.000000282 0 0.000000
59 0 0.000000347 0 0.000000351 0 0.000000
19 0 0.00000023 0 0.00000098 0 0.00000063 0 0.00000043 0 0.000000
304 0 0.000000263 0 0.000000106 0 0.000000
7 0 0.0000003 0 0.000000
27 0 0.00000011 0 0.000000
359 0 0.00000047 0 0.00000015 0 0.000000
298 0 0.000000355 0 0.000000
31 0 0.000000243 0 0.000000343 0 0.000000
82 0 0.000000128 0 0.000000279 0 0.000000339 0 0.000000320 0 0.000000257 0 0.000000327 0 0.000000314 0 0.000000295 0 0.000000311 0 0.000000
259 0 0.00000066 0 0.000000
323 0 0.000000120 0 0.000000
90 0 0.000000137 0 0.000000104 0 0.000000232 0 0.000000307 0 0.000000136 0 0.000000275 0 0.000000
88 0 0.000000291 0 0.000000330 0 0.000000336 0 0.000000
50 0 0.000000112 0 0.000000
72 0 0.000000273 0 0.000000
56 0 0.00000034 0 0.00000074 0 0.000000
145 0 0.000000346 0 0.000000
40 0 0.000000352 0 0.000000
18 0 0.00000024 0 0.00000096 0 0.00000058 0 0.000000
8 0 0.0000002 0 0.000000
360 0 0.00000042 0 0.00000010 0 0.000000
289 0 0.00000026 0 0.000000
210 0 0.00000080 0 0.00000016 0 0.000000
249 0 0.000000354 0 0.000000
32 0 0.000000233 0 0.000000
64 0 0.000000
248 0 0.000000181 0 0.000000
48 0 0.000000265 0 0.000000344 0 0.000000305 0 0.000000281 0 0.000000152 0 0.000000338 0 0.000000328 0 0.000000129 0 0.000000264 0 0.000000312 0 0.000000297 0 0.000000121 0 0.000000296 0 0.000000322 0 0.000000280 0 0.000000113 0 0.000000321 0 0.000000217 0 0.000000313 0 0.000000
97 0 0.000000306 0 0.000000
81 0 0.000000329 0 0.000000
65 0 0.000000337 0 0.000000290 0 0.000000
49 0 0.000000105 0 0.000000226 0 0.000000274 0 0.000000
33 0 0.000000345 0 0.000000353 0 0.000000
17 0 0.00000057 0 0.00000041 0 0.000000
258 0 0.00000025 0 0.00000089 0 0.00000073 0 0.000000
242 0 0.0000009 0 0.000000
1 0 0.000000
Degree Radian Amplitude Amp Multiplier Wave 10 0 Degree 01 0.017453 0 02 0.034907 03 0.05236 Radians 04 0.069813 0 05 0.087266 06 0.10472 Sin 07 0.122173 0 1 08 0.139626 0 2 09 0.15708 0 3 0
10 0.174533 0 4 011 0.191986 0 5 012 0.20944 0 6 013 0.226893 0 7 014 0.244346 0 8 015 0.261799 0 9 016 0.279253 0 10 017 0.296706 0 11 018 0.314159 0 12 019 0.331613 0 13 020 0.349066 0 14 021 0.366519 0 15 022 0.383972 0 16 023 0.401426 0 17 024 0.418879 0 18 025 0.436332 0 19 026 0.453786 0 20 027 0.471239 0 21 028 0.488692 0 22 029 0.506145 0 23 030 0.523599 0 24 031 0.541052 032 0.558505 033 0.575959 034 0.593412 035 0.610865 036 0.628319 037 0.645772 038 0.663225 039 0.680678 040 0.698132 041 0.715585 042 0.733038 043 0.750492 0
44 0.767945 045 0.785398 046 0.802851 047 0.820305 048 0.837758 049 0.855211 050 0.872665 051 0.890118 052 0.907571 053 0.925025 054 0.942478 055 0.959931 056 0.977384 057 0.994838 058 1.012291 059 1.029744 060 1.047198 061 1.064651 062 1.082104 063 1.099557 064 1.117011 065 1.134464 066 1.151917 067 1.169371 068 1.186824 069 1.204277 070 1.22173 071 1.239184 072 1.256637 073 1.27409 074 1.291544 075 1.308997 076 1.32645 077 1.343904 078 1.361357 079 1.37881 080 1.396263 081 1.413717 082 1.43117 083 1.448623 084 1.466077 085 1.48353 086 1.500983 087 1.518436 088 1.53589 0
89 1.553343 090 1.570796 091 1.58825 092 1.605703 093 1.623156 094 1.640609 095 1.658063 096 1.675516 097 1.692969 098 1.710423 099 1.727876 0
100 1.745329 0101 1.762783 0102 1.780236 0103 1.797689 0104 1.815142 0105 1.832596 0106 1.850049 0107 1.867502 0108 1.884956 0109 1.902409 0110 1.919862 0111 1.937315 0112 1.954769 0113 1.972222 0114 1.989675 0115 2.007129 0116 2.024582 0117 2.042035 0118 2.059489 0119 2.076942 0120 2.094395 0121 2.111848 0122 2.129302 0123 2.146755 0124 2.164208 0125 2.181662 0126 2.199115 0127 2.216568 0128 2.234021 0129 2.251475 0130 2.268928 0131 2.286381 0132 2.303835 0133 2.321288 0
134 2.338741 0135 2.356194 0136 2.373648 0137 2.391101 0138 2.408554 0139 2.426008 0140 2.443461 0141 2.460914 0142 2.478368 0143 2.495821 0144 2.513274 0145 2.530727 0146 2.548181 0147 2.565634 0148 2.583087 0149 2.600541 0150 2.617994 0151 2.635447 0152 2.6529 0153 2.670354 0154 2.687807 0155 2.70526 0156 2.722714 0157 2.740167 0158 2.75762 0159 2.775074 0160 2.792527 0161 2.80998 0162 2.827433 0163 2.844887 0164 2.86234 0165 2.879793 0166 2.897247 0167 2.9147 0168 2.932153 0169 2.949606 0170 2.96706 0171 2.984513 0172 3.001966 0173 3.01942 0174 3.036873 0175 3.054326 0176 3.071779 0177 3.089233 0178 3.106686 0
179 3.124139 0180 3.141593 0181 3.159046 0182 3.176499 0183 3.193953 0184 3.211406 0185 3.228859 0186 3.246312 0187 3.263766 0188 3.281219 0189 3.298672 0190 3.316126 0191 3.333579 0192 3.351032 0193 3.368485 0194 3.385939 0195 3.403392 0196 3.420845 0197 3.438299 0198 3.455752 0199 3.473205 0200 3.490659 0201 3.508112 0202 3.525565 0203 3.543018 0204 3.560472 0205 3.577925 0206 3.595378 0207 3.612832 0208 3.630285 0209 3.647738 0210 3.665191 0211 3.682645 0212 3.700098 0213 3.717551 0214 3.735005 0215 3.752458 0216 3.769911 0217 3.787364 0218 3.804818 0219 3.822271 0220 3.839724 0221 3.857178 0222 3.874631 0223 3.892084 0
224 3.909538 0225 3.926991 0226 3.944444 0227 3.961897 0228 3.979351 0229 3.996804 0230 4.014257 0231 4.031711 0232 4.049164 0233 4.066617 0234 4.08407 0235 4.101524 0236 4.118977 0237 4.13643 0238 4.153884 0239 4.171337 0240 4.18879 0241 4.206243 0242 4.223697 0243 4.24115 0244 4.258603 0245 4.276057 0246 4.29351 0247 4.310963 0248 4.328417 0249 4.34587 0250 4.363323 0251 4.380776 0252 4.39823 0253 4.415683 0254 4.433136 0255 4.45059 0256 4.468043 0257 4.485496 0258 4.502949 0259 4.520403 0260 4.537856 0261 4.555309 0262 4.572763 0263 4.590216 0264 4.607669 0265 4.625123 0266 4.642576 0267 4.660029 0268 4.677482 0
269 4.694936 0270 4.712389 0271 4.729842 0272 4.747296 0273 4.764749 0274 4.782202 0275 4.799655 0276 4.817109 0277 4.834562 0278 4.852015 0279 4.869469 0280 4.886922 0281 4.904375 0282 4.921828 0283 4.939282 0284 4.956735 0285 4.974188 0286 4.991642 0287 5.009095 0288 5.026548 0289 5.044002 0290 5.061455 0291 5.078908 0292 5.096361 0293 5.113815 0294 5.131268 0295 5.148721 0296 5.166175 0297 5.183628 0298 5.201081 0299 5.218534 0300 5.235988 0301 5.253441 0302 5.270894 0303 5.288348 0304 5.305801 0305 5.323254 0306 5.340708 0307 5.358161 0308 5.375614 0309 5.393067 0310 5.410521 0311 5.427974 0312 5.445427 0313 5.462881 0
314 5.480334 0315 5.497787 0316 5.51524 0317 5.532694 0318 5.550147 0319 5.5676 0320 5.585054 0321 5.602507 0322 5.61996 0323 5.637413 0324 5.654867 0325 5.67232 0326 5.689773 0327 5.707227 0328 5.72468 0329 5.742133 0330 5.759587 0331 5.77704 0332 5.794493 0333 5.811946 0334 5.8294 0335 5.846853 0336 5.864306 0337 5.88176 0338 5.899213 0339 5.916666 0340 5.934119 0341 5.951573 0342 5.969026 0343 5.986479 0344 6.003933 0345 6.021386 0346 6.038839 0347 6.056293 0348 6.073746 0349 6.091199 0350 6.108652 0351 6.126106 0352 6.143559 0353 6.161012 0354 6.178466 0355 6.195919 0356 6.213372 0357 6.230825 0358 6.248279 0
359 6.265732 0360 6.283185 0
Wave 2 wave 3 wave 4 wave 5 wave 6 wave 7 wave 8 wave 90 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 0
0 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 0
0 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 0
0 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 0
0 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 0
0 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 0
0 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 0
0 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 0
0 0 0 0 0 0 0 00 0 0 0 0 0 0 0
wave 10 wave 11 wave 12 wave 13 wave 14 wave 15 wave 16 wave 170 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 0
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123456789
10111213141516171819202122232425262728293031323334
353637383940414243444546474849505152535455565758596061626364656667686970717273747576777879
8081828384858687888990919293949596979899
100101102103104105106107108109110111112113114115116117118119120121122123124
125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169
170171172173174175176177178179180181182183184185186187188189190191192193194195196197198199200201202203204205206207208209210211212213214
215216217218219220221222223224225226227228229230231232233234235236237238239240241242243244245246247248249250251252253254255256
1 100.00%2 100.00%3 100.00%4 100.00%5 100.00%6 100.00%7 100.00%8 100.00%9 100.00%
10 100.00%11 100.00%12 100.00%13 100.00%14 100.00%15 100.00%16 100.00%17 100.00%18 100.00%19 100.00%20 100.00%21 100.00%22 100.00%23 100.00%24 100.00%
frequency Wavelength 1/4 wave
1 1 1/ 4 1/ 4 0.78539750002 2 1/ 2 1/ 2 3.14159000003 3 3/ 4 3/ 4 7.06857750004 4 1 1 12.56636000005 5 1 1/ 4 1 1/ 4 19.63493750006 6 1 1/ 2 1 1/ 2 28.27431000007 7 1 3/ 4 1 3/ 4 38.48447750008 8 2 2 50.26544000009 9 2 1/ 4 2 1/ 4 63.6171975000
10 10 2 1/ 2 2 1/ 2 78.539750000011 11 2 3/ 4 2 3/ 4 95.033097500012 12 3 3 113.0972400000
Radius of equilibrium
(RE)
Area of Sphere @ RE
Area of E sphere
0.0654497917 1/16 1/ 8 0.04908734380.5235983333 1/ 8 1/ 4 0.19634937501.7671443750 3/16 3/ 8 0.44178609384.1887866667 1/ 4 1/ 2 0.78539750008.1812239583 5/16 5/ 8 1.2271835938
14.1371550000 3/ 8 3/ 4 1.767144375022.4492785417 7/16 7/ 8 2.405279843833.5102933333 1/ 2 1 3.141590000047.7128981250 9/16 1 1/ 8 3.976074843865.4497916667 5/ 8 1 1/ 4 4.908734375087.1136727083 11/16 1 3/ 8 5.9395685938
113.0972400000 3/ 4 1 1/ 2 7.0685775000
Volume of sphere @ RE
New Radius for E field
New Radius for B field
Volume of B sphere
0.0081812240 0.25000 0.19531 0.78125 4.000000.0654497917 0.50000 0.78125 3.12500 4.000000.2208930469 0.75000 1.75781 7.03125 4.000000.5235983333 1.00000 3.12500 12.50000 4.000001.0226529948 1.25000 4.88281 19.53125 4.000001.7671443750 1.50000 7.03125 28.12500 4.000002.8061598177 1.75000 9.57031 38.28125 4.000004.1887866667 2.00000 12.50000 50.00000 4.000005.9641122656 2.25000 15.82031 63.28125 4.000008.1812239583 2.50000 19.53125 78.12500 4.00000
10.8892090885 2.75000 23.63281 94.53125 4.0000014.1371550000 3.00000 28.12500 112.50000 4.00000
Radius of equilibrium
(RE)