WaveSum - Adding Two Sine Waves We add together A*sin(k_1*x...

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Unformatted text preview: Adding Two Sine Waves We add together A*sin(k_1*x - omega_1*t) and B*sin(k_2*x - omega_2*t) A= k_1= omega_1= B= k_2= omega_2= 1 3 3 1 3 -3 delt a_x= delt a_t = 0.01 0.01 t= 16.52 3 2 1 0 0 0.5 1 1.5 2 2.5 3 3.5 4 4 .5 5 -1 -2 -3 1652 Animat e t he wave by clicking and holding on t he end of t he slider bar The idea of using a slider for animation is from Michael J. Moloney, Rose-Hulman Institute of Technology Position x Wave 0 0.648401 0.01 0.670945 0.02 0.692885 0.03 0.714201 0.04 0.734875 0.05 0.754887 0.06 0.77422 0.07 0.792857 0.08 0.810779 0.09 0.827973 0.1 0.844421 0.11 0.860109 0.12 0.875023 0.13 0.889149 0.14 0.902476 0.15 0.91499 0.16 0.926681 0.17 0.937537 0.18 0.94755 0.19 0.956711 0.2 0.96501 0.21 0.972441 0.22 0.978997 0.23 0.984672 0.24 0.989461 0.25 0.993359 0.26 0.996363 0.27 0.998471 0.28 0.99968 0.29 0.999989 0.3 0.999398 0.31 0.997909 0.32 0.995521 0.33 0.992237 0.34 0.98806 0.35 0.982994 0.36 0.977043 0.37 0.970213 0.38 0.96251 0.39 0.953941 0.4 0.944513 0.41 0.934236 0.42 0.923117 0.43 0.911168 0.44 0.898399 0.45 0.884821 0.46 0.870447 0.47 0.85529 0.48 0.839363 0.49 0.822681 0.5 0.805258 0.51 0.78711 0.52 0.768255 0.53 0.748708 0.54 0.728487 0.55 0.70761 0.56 0.686097 0.57 0.663966 0.58 0.641238 0.59 0.617932 0.6 0.594071 0.61 0.569675 0.62 0.544766 0.63 0.519367 0.64 0.493501 0.65 0.46719 0.66 0.440459 0.67 0.413332 0.68 0.385833 0.69 0.357986 0.7 0.329817 0.71 0.301352 0.72 0.272615 0.73 0.243633 0.74 0.214432 0.75 0.185038 0.76 0.155477 0.77 0.125776 0.78 0.095962 0.79 0.066062 0.8 0.036102 0.81 0.00611 0.82 -0.02389 0.83 -0.05386 0.84 -0.08379 0.85 -0.11364 0.86 -0.14339 0.87 -0.17301 0.88 -0.20248 0.89 -0.23176 0.9 -0.26084 0.91 -0.28968 0.92 -0.31826 0.93 -0.34655 0.94 -0.37453 0.95 -0.40217 0.96 -0.42946 0.97 -0.45635 0.98 -0.48284 0.99 -0.50889 1 -0.53448 1.01 -0.55959 1.02 -0.5842 1.03 -0.60828 1.04 -0.63181 1.05 -0.65478 1.06 -0.67716 1.07 -0.69892 1.08 -0.72006 1.09 -0.74055 1.1 -0.76037 1.11 -0.77951 1.12 -0.79795 1.13 -0.81567 1.14 -0.83266 1.15 -0.84889 1.16 -0.86437 1.17 -0.87906 1.18 -0.89297 1.19 -0.90606 1.2 -0.91835 1.21 -0.92981 1.22 -0.94043 1.23 -0.9502 1.24 -0.95912 1.25 -0.96718 1.26 -0.97437 1.27 -0.98068 1.28 -0.9861 1.29 -0.99064 1.3 -0.99429 1.31 -0.99704 1.32 -0.9989 1.33 -0.99986 1.34 -0.99991 1.35 -0.99907 1.36 -0.99733 1.37 -0.99469 1.38 -0.99116 1.39 -0.98673 1.4 -0.98142 1.41 -0.97522 1.42 -0.96814 1.43 -0.9602 1.44 -0.95139 1.45 -0.94172 1.46 -0.9312 1.47 -0.91985 1.48 -0.90767 1.49 -0.89467 1.5 -0.88087 1.51 -0.86628 1.52 -0.8509 1.53 -0.83476 1.54 -0.81787 1.55 -0.80024 1.56 -0.7819 1.57 -0.76285 1.58 -0.74311 1.59 -0.7227 1.6 -0.70164 1.61 -0.67996 1.62 -0.65766 1.63 -0.63476 1.64 -0.6113 1.65 -0.58729 1.66 -0.56275 1.67 -0.5377 1.68 -0.51216 1.69 -0.48617 1.7 -0.45974 1.71 -0.4329 1.72 -0.40566 1.73 -0.37806 1.74 -0.35012 1.75 -0.32187 1.76 -0.29332 1.77 -0.26452 1.78 -0.23547 1.79 -0.20621 1.8 -0.17677 1.81 -0.14717 1.82 -0.11743 1.83 -0.08759 1.84 -0.05767 1.85 -0.0277 1.86 0.002297 1.87 0.032292 1.88 0.062257 1.89 0.092166 1.9 0.121993 1.91 0.151709 1.92 0.181289 1.93 0.210706 1.94 0.239933 1.95 0.268945 1.96 0.297714 1.97 0.326215 1.98 0.354423 1.99 0.382312 2 0.409857 2.01 0.437033 2.02 0.463816 2.03 0.490181 2.04 0.516105 2.05 0.541565 2.06 0.566537 2.07 0.590999 2.08 0.61493 2.09 0.638307 2.1 0.66111 2.11 0.683318 2.12 0.704911 2.13 0.725869 2.14 0.746174 2.15 0.765808 2.16 0.784753 2.17 0.802991 2.18 0.820507 2.19 0.837284 2.2 0.853308 2.21 0.868564 2.22 0.883038 2.23 0.896718 2.24 0.90959 2.25 0.921644 2.26 0.932869 2.27 0.943254 2.28 0.95279 2.29 0.961469 2.3 0.969283 2.31 0.976224 2.32 0.982287 2.33 0.987465 2.34 0.991755 2.35 0.995153 2.36 0.997655 2.37 0.999259 2.38 0.999964 2.39 0.999769 2.4 0.998674 2.41 0.996681 2.42 0.99379 2.43 0.990005 2.44 0.98533 2.45 0.979767 2.46 0.973323 2.47 0.966003 2.48 0.957814 2.49 0.948762 2.5 0.938857 2.51 0.928107 2.52 0.916522 2.53 0.904111 2.54 0.890888 2.55 0.876862 2.56 0.862047 2.57 0.846457 2.58 0.830105 2.59 0.813006 2.6 0.795175 2.61 0.776628 2.62 0.757383 2.63 0.737456 2.64 0.716865 2.65 0.695629 2.66 0.673767 2.67 0.651299 2.68 0.628245 2.69 0.604625 2.7 0.580462 2.71 0.555775 2.72 0.530589 2.73 0.504925 2.74 0.478807 2.75 0.452258 2.76 0.425302 2.77 0.397963 2.78 0.370266 2.79 0.342236 2.8 0.313898 2.81 0.285277 2.82 0.2564 2.83 0.227292 2.84 0.197979 2.85 0.168488 2.86 0.138845 2.87 0.109078 2.88 0.079212 2.89 0.049276 2.9 0.019294 2.91 -0.0107 2.92 -0.04069 2.93 -0.07065 2.94 -0.10053 2.95 -0.13033 2.96 -0.16001 2.97 -0.18955 2.98 -0.21892 2.99 -0.24809 3 -0.27703 3.01 -0.30573 3.02 -0.33415 3.03 -0.36227 3.04 -0.39007 3.05 -0.41751 3.06 -0.44458 3.07 -0.47125 3.08 -0.49749 3.09 -0.52329 3.1 -0.54861 3.11 -0.57344 3.12 -0.59776 3.13 -0.62154 3.14 -0.64476 3.15 -0.66739 3.16 -0.68943 3.17 -0.71085 3.18 -0.73163 3.19 -0.75175 3.2 -0.77119 3.21 -0.78994 3.22 -0.80797 3.23 -0.82528 3.24 -0.84185 3.25 -0.85766 3.26 -0.8727 3.27 -0.88695 3.28 -0.90041 3.29 -0.91305 3.3 -0.92487 3.31 -0.93586 3.32 -0.94601 3.33 -0.95531 3.34 -0.96375 3.35 -0.97132 3.36 -0.97801 3.37 -0.98383 3.38 -0.98876 3.39 -0.9928 3.4 -0.99594 3.41 -0.9982 3.42 -0.99955 3.43 -1 3.44 -0.99955 3.45 -0.99821 3.46 -0.99596 3.47 -0.99282 3.48 -0.98878 3.49 -0.98386 3.5 -0.97805 3.51 -0.97136 3.52 -0.9638 3.53 -0.95536 3.54 -0.94607 3.55 -0.93593 3.56 -0.92494 3.57 -0.91313 3.58 -0.90049 3.59 -0.88704 3.6 -0.87279 3.61 -0.85776 3.62 -0.84195 3.63 -0.82539 3.64 -0.80808 3.65 -0.79005 3.66 -0.7713 3.67 -0.75187 3.68 -0.73175 3.69 -0.71098 3.7 -0.68956 3.71 -0.66753 3.72 -0.6449 3.73 -0.62168 3.74 -0.59791 3.75 -0.5736 3.76 -0.54877 3.77 -0.52344 3.78 -0.49765 3.79 -0.47141 3.8 -0.44474 3.81 -0.41768 3.82 -0.39024 3.83 -0.36244 3.84 -0.33432 3.85 -0.3059 3.86 -0.27721 3.87 -0.24826 3.88 -0.2191 3.89 -0.18973 3.9 -0.16019 3.91 -0.13051 3.92 -0.10072 3.93 -0.07083 3.94 -0.04088 3.95 -0.01089 3.96 0.019111 3.97 0.049092 3.98 0.079029 3.99 0.108895 4 0.138664 4.01 0.168307 4.02 0.197799 4.03 0.227113 4.04 0.256222 4.05 0.285101 4.06 0.313723 4.07 0.342063 4.08 0.370096 4.09 0.397795 4.1 0.425136 4.11 0.452094 4.12 0.478646 4.13 0.504767 4.14 0.530433 4.15 0.555623 4.16 0.580312 4.17 0.604479 4.18 0.628102 4.19 0.65116 4.2 0.673632 4.21 0.695497 4.22 0.716737 4.23 0.737332 4.24 0.757263 4.25 0.776512 4.26 0.795063 4.27 0.812899 4.28 0.830002 4.29 0.846359 4.3 0.861954 4.31 0.876774 4.32 0.890804 4.33 0.904033 4.34 0.916448 4.35 0.928039 4.36 0.938794 4.37 0.948704 4.38 0.957761 4.39 0.965956 4.4 0.973281 4.41 0.979731 4.42 0.985298 4.43 0.98998 4.44 0.99377 4.45 0.996666 4.46 0.998665 4.47 0.999765 4.48 0.999965 4.49 0.999266 4.5 0.997667 4.51 0.995171 4.52 0.991779 4.53 0.987494 4.54 0.982321 4.55 0.976264 4.56 0.969328 4.57 0.96152 4.58 0.952846 4.59 0.943315 4.6 0.932935 4.61 0.921716 4.62 0.909667 4.63 0.896799 4.64 0.883124 4.65 0.868655 4.66 0.853404 4.67 0.837385 4.68 0.820612 4.69 0.803101 4.7 0.784867 4.71 0.765926 4.72 0.746297 4.73 0.725995 4.74 0.705041 4.75 0.683452 4.76 0.661248 4.77 0.638449 4.78 0.615075 4.79 0.591148 4.8 0.566688 4.81 0.541719 -0.6484 -0.62527 -0.60158 -0.57735 -0.5526 -0.52735 -0.50163 -0.47546 -0.44885 -0.42185 -0.39446 -0.36672 -0.33865 -0.31028 -0.28162 -0.25271 -0.22358 -0.19424 -0.16473 -0.13507 -0.10529 -0.07541 -0.04547 -0.01548 0.014517 0.044503 0.074449 0.104327 0.134112 0.163776 0.193293 0.222636 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