WaveSumBeats

WaveSumBeats - Adding Two Close Sine Waves: Beats, Group...

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Unformatted text preview: Adding Two Close Sine Waves: Beats, Group Velocity and Phase Velocity 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 3.3 delt a_x= delt a_t = 0.1 0.1 t= 41.7 3 2 1 0 0 5 10 15 20 25 30 35 40 45 -1 -2 -3 417 Position x Wave 0 0.534323 0.1 0.760255 0.2 0.918277 0.3 0.994271 0.4 0.981451 0.5 0.88096 0.6 0.701775 0.7 0.459903 0.8 0.17695 0.9 -0.12181 1 -0.40969 1.1 -0.66097 1.2 -0.85321 1.3 -0.96924 1.4 -0.99868 1.5 -0.93892 1.6 -0.79529 1.7 -0.58061 1.8 -0.31407 1.9 -0.01948 2 0.276856 2.1 0.54846 2.2 0.771071 2.3 0.924804 2.4 0.995928 2.5 0.978088 2.6 0.872879 2.7 0.689698 2.8 0.444908 2.9 0.160376 3 -0.13848 3.1 -0.42497 3.2 -0.6735 3.3 -0.86186 3.4 -0.97324 3.5 -0.99768 3.6 -0.933 3.7 -0.78498 3.8 -0.56684 3.9 -0.29806 4 -0.00266 4.1 0.292974 4.2 0.562441 4.3 0.781668 4.4 0.93107 4.5 0.997303 4.6 0.97445 4.7 0.864551 4.8 0.677426 4.9 0.429787 5 0.143757 5.1 -0.15511 5.2 -0.44013 5.3 -0.68583 5.4 -0.87027 5.5 -0.97696 5.6 -0.99639 5.7 -0.92682 5.8 -0.77445 5.9 -0.55291 6 -0.28197 6.1 0.01415 6.2 0.309008 6.3 0.576264 6.4 0.792044 6.5 0.937073 6.6 0.998396 6.7 0.970535 6.8 0.85598 6.9 0.664962 7 0.414545 7.1 0.127098 7.2 -0.1717 7.3 -0.45517 7.4 -0.69797 7.5 -0.87843 7.6 -0.98041 7.7 -0.99483 7.8 -0.92037 7.9 -0.76371 8 -0.53882 8.1 -0.2658 8.2 0.03096 8.3 0.324956 8.4 0.589924 8.5 0.802196 8.6 0.942811 8.7 0.999207 8.8 0.966347 8.9 0.847166 9 0.65231 9.1 0.399185 9.2 0.110402 9.3 -0.18824 9.4 -0.47007 9.5 -0.70991 9.6 -0.88634 9.7 -0.98359 9.8 -0.99298 9.9 -0.91367 10 -0.75274 10.1 -0.52458 10.2 -0.24955 10.3 0.047761 10.4 0.340811 10.5 0.603417 10.6 0.812122 10.7 0.948282 10.8 0.999735 10.9 0.961885 11 0.838112 11.1 0.639473 11.2 0.383712 11.3 0.093676 11.4 -0.20473 11.5 -0.48485 11.6 -0.72165 11.7 -0.894 11.8 -0.98648 11.9 -0.99085 12 -0.90671 12.1 -0.74157 12.2 -0.51019 12.3 -0.23324 12.4 0.064549 12.5 0.35657 12.6 0.61674 12.7 0.821818 12.8 0.953485 12.9 0.999981 13 0.957151 13.1 0.828822 13.2 0.626456 13.3 0.368131 13.4 0.076922 13.5 -0.22116 13.6 -0.49948 13.7 -0.73319 13.8 -0.9014 13.9 -0.9891 14 -0.98844 14.1 -0.89949 14.2 -0.73018 14.3 -0.49566 14.4 -0.21685 14.5 0.081319 14.6 0.372229 14.7 0.629888 14.8 0.831281 14.9 0.958419 15 0.999944 15.1 0.952146 15.2 0.819297 15.3 0.613262 15.4 0.352446 15.5 0.060147 15.6 -0.23752 15.7 -0.51398 15.8 -0.74452 15.9 -0.90856 16 -0.99143 16.1 -0.98575 16.2 -0.89201 16.3 -0.71859 16.4 -0.48098 16.5 -0.20041 16.6 0.098066 16.7 0.387782 16.8 0.642858 16.9 0.84051 17 0.963082 17.1 0.999624 17.2 0.946873 17.3 0.80954 17.4 0.599894 17.5 0.336661 17.6 0.043355 17.7 -0.25382 17.8 -0.52833 17.9 -0.75564 18 -0.91545 18.1 -0.99349 18.2 -0.98278 18.3 -0.88429 18.4 -0.7068 18.5 -0.46617 18.6 -0.18391 18.7 0.114785 18.8 0.403225 18.9 0.655646 19 0.849501 19.1 0.967472 19.2 0.999021 19.3 0.941332 19.4 0.799555 19.5 0.586357 19.6 0.320781 19.7 0.026551 19.8 -0.27005 19.9 -0.54253 20 -0.76655 20.1 -0.92209 20.2 -0.99527 20.3 -0.97954 20.4 -0.87631 20.5 -0.6948 20.6 -0.45123 20.7 -0.16736 20.8 0.131471 20.9 0.418554 21 0.668249 21.1 0.858252 21.2 0.971589 21.3 0.998137 21.4 0.935524 21.5 0.789344 21.6 0.572654 21.7 0.304811 21.8 0.009739 21.9 -0.2862 22 -0.55658 22.1 -0.77724 22.2 -0.92847 22.3 -0.99676 22.4 -0.97601 22.5 -0.86809 22.6 -0.68261 22.7 -0.43616 22.8 -0.15076 22.9 0.148121 23 0.433766 23.1 0.680663 23.2 0.86676 23.3 0.975431 23.4 0.99697 23.5 0.929452 23.6 0.778909 23.7 0.558789 23.8 0.288754 23.9 -0.00708 24 -0.30227 24.1 -0.57047 24.2 -0.78771 24.3 -0.93458 24.4 -0.99797 24.5 -0.97222 24.6 -0.85962 24.7 -0.67023 24.8 -0.42097 24.9 -0.13411 25 0.164728 25.1 0.448854 25.2 0.692885 25.3 0.875023 25.4 0.978997 25.5 0.995521 25.6 0.923117 25.7 0.768255 25.8 0.544766 25.9 0.272615 26 -0.02389 26.1 -0.31826 26.2 -0.5842 26.3 -0.79795 26.4 -0.94043 26.5 -0.9989 26.6 -0.96814 26.7 -0.8509 26.8 -0.65766 26.9 -0.40566 27 -0.11743 27.1 0.181289 27.2 0.463816 27.3 0.704911 27.4 0.883038 27.5 0.982287 27.6 0.99379 27.7 0.916522 27.8 0.757383 27.9 0.530589 28 0.2564 28.1 -0.04069 28.2 -0.33415 28.3 -0.59776 28.4 -0.80797 28.5 -0.94601 28.6 -0.99955 28.7 -0.9638 28.8 -0.84195 28.9 -0.6449 29 -0.39024 29.1 -0.10072 29.2 0.197799 29.3 0.478646 29.4 0.716737 29.5 0.890804 29.6 0.985298 29.7 0.991779 29.8 0.909667 29.9 0.746297 30 0.516262 30.1 0.240112 30.2 -0.05749 30.3 -0.34995 30.4 -0.61116 30.5 -0.81777 30.6 -0.95133 30.7 -0.99991 30.8 -0.95918 30.9 -0.83276 31 -0.63196 31.1 -0.3747 31.2 -0.08397 31.3 0.214253 31.4 0.493341 31.5 0.728361 31.6 0.898318 31.7 0.988032 31.8 0.989487 31.9 0.902555 32 0.735 32.1 0.501789 32.2 0.223756 32.3 -0.07427 32.4 -0.36565 32.5 -0.62438 32.6 -0.82733 32.7 -0.95638 32.8 -0.99999 32.9 -0.95429 33 -0.82333 33.1 -0.61884 33.2 -0.35906 33.3 -0.06721 33.4 0.230646 33.5 0.507897 33.6 0.739779 33.7 0.905578 33.8 0.990486 33.9 0.986916 34 0.895187 34.1 0.723495 34.2 0.487175 34.3 0.207336 34.4 -0.09102 34.5 -0.38125 34.6 -0.63742 34.7 -0.83666 34.8 -0.96115 34.9 -0.99979 35 -0.94912 35.1 -0.81367 35.2 -0.60554 35.3 -0.34331 35.4 -0.05042 35.5 0.246974 35.6 0.522309 35.7 0.750987 35.8 0.912582 35.9 0.992659 36 0.984065 36.1 0.887567 36.2 0.711785 36.3 0.472422 36.4 0.190859 36.5 -0.10775 36.6 -0.39674 36.7 -0.65029 36.8 -0.84575 36.9 -0.96566 37 -0.99931 37.1 -0.9437 37.2 -0.80378 37.3 -0.59207 37.4 -0.32747 37.5 -0.03362 37.6 0.263232 37.7 0.536573 37.8 0.761984 37.9 0.919329 38 0.994553 38.1 0.980936 38.2 0.879696 38.3 0.699875 38.4 0.457536 38.5 0.174327 38.6 -0.12445 38.7 -0.41212 38.8 -0.66297 38.9 -0.8546 39 -0.96989 39.1 -0.99854 39.2 -0.938 39.3 -0.79367 39.4 -0.57844 39.5 -0.31154 39.6 -0.01681 39.7 0.279415 39.8 0.550686 39.9 0.772764 40 0.925815 40.1 0.996165 40.2 0.97753 40.3 0.871576 40.4 0.687766 40.5 0.44252 40.6 0.157746 40.7 -0.14112 40.8 -0.42738 40.9 -0.67546 41 -0.86321 41.1 -0.97385 41.2 -0.99749 41.3 -0.93204 41.4 -0.78333 41.5 -0.56464 41.6 -0.29552 41.7 9.5E-013 41.8 0.29552 41.9 0.564642 42 0.783327 42.1 0.932039 42.2 0.997495 42.3 0.973848 42.4 0.863209 42.5 0.675463 42.6 0.42738 42.7 0.14112 42.8 -0.15775 42.9 -0.44252 43 -0.68777 43.1 -0.87158 43.2 -0.97753 43.3 -0.99616 43.4 -0.92581 43.5 -0.77276 43.6 -0.55069 43.7 -0.27942 43.8 0.016814 43.9 0.311541 44 0.57844 44.1 0.793668 44.2 0.938 44.3 0.998543 44.4 0.96989 44.5 0.854599 44.6 0.662969 44.7 0.412118 44.8 0.124454 44.9 -0.17433 45 -0.45754 45.1 -0.69987 45.2 -0.8797 45.3 -0.98094 45.4 -0.99455 45.5 -0.91933 45.6 -0.76198 45.7 -0.53657 45.8 -0.26323 45.9 0.033623 46 0.327474 46.1 0.592074 46.2 0.803784 46.3 0.943696 46.4 0.999309 46.5 0.965658 46.6 0.845747 46.7 0.650288 46.8 0.396741 46.9 0.107754 47 -0.19086 47.1 -0.47242 47.2 -0.71179 47.3 -0.88757 47.4 -0.98407 47.5 -0.99266 47.6 -0.91258 47.7 -0.75099 47.8 -0.52231 47.9 -0.24697 48 0.050423 48.1 0.343315 0.581098 0.81346 0.958038 0.999229 0.932587 0.765306 0.515436 0.209942 -0.11821 -0.4336 -0.7022 -0.89502 -0.99126 -0.98052 -0.86397 -0.65419 -0.37381 -0.05308 0.273367 0.570317 0.805721 0.954175 0.99966 0.937265 0.773726 0.526689 0.222815 -0.1051 -0.42168 -0.69275 -0.88907 -0.98943 -0.98303 -0.87054 -0.6641 -0.386 -0.06625 0.26066 0.559437 0.797841 0.950147 0.999917 0.94178 0.782011 0.537851 0.235649 -0.09198 -0.40969 -0.68318 -0.88295 -0.98744 -0.98536 -0.87695 -0.6739 -0.39813 -0.0794 0.247909 0.54846 0.789823 0.945953 1 0.946132 0.790161 0.54892 0.248442 -0.07885 -0.39763 -0.6735 -0.87669 -0.98527 -0.98752 -0.88321 -0.68359 -0.41019 -0.09253 0.235114 0.537387 0.781668 0.941595 0.999909 0.950318 0.798173 0.559893 0.261192 -0.0657 -0.38549 -0.66369 -0.87027 -0.98293 -0.98951 -0.88932 -0.69315 -0.42218 -0.10565 0.222278 0.526221 0.773377 0.937073 0.999645 0.95434 0.806047 0.570769 0.273897 -0.05253 -0.37329 -0.65377 -0.8637 -0.98041 -0.99133 -0.89527 -0.70259 -0.4341 -0.11875 0.209404 0.514963 0.764951 0.932388 0.999207 0.958196 0.81378 0.581546 0.286554 -0.03936 -0.36103 -0.64374 -0.85698 -0.97773 -0.99298 -0.90107 -0.71191 -0.44594 -0.13184 0.196493 0.503616 0.756392 0.927541 0.998595 0.961885 0.821372 0.592222 0.299161 -0.02618 -0.3487 -0.63359 -0.85011 -0.97488 -0.99445 -0.90671 -0.72111 -0.4577 -0.14489 0.183548 0.492182 0.747702 0.922533 0.997809 0.965407 0.828822 0.602794 0.311716 -0.013 -0.33632 -0.62334 -0.84309 -0.97186 -0.99575 -0.91219 -0.73018 -0.46938 -0.15793 0.170571 0.480662 0.738882 0.917365 0.99685 0.968761 0.836127 0.613262 0.324217 0.000184 -0.32387 -0.61297 -0.83593 -0.96867 -0.99688 -0.91751 -0.73913 -0.48098 -0.17093 0.157564 0.469058 0.729933 0.912037 0.995718 0.971946 0.843286 0.623623 0.336661 0.013369 -0.31137 -0.6025 -0.82862 -0.96531 -0.99783 -0.92268 -0.74795 -0.4925 -0.18391 0.14453 0.457373 0.720857 0.90655 0.994413 0.974963 0.8503 0.633876 0.349047 0.026551 -0.29881 -0.59193 -0.82116 -0.96178 -0.99861 -0.92768 -0.75663 -0.50393 -0.19685 0.131471 0.445608 0.711656 0.900906 0.992935 0.97781 0.857165 0.644018 0.361373 0.039729 -0.2862 -0.58125 -0.81357 -0.95809 -0.99922 -0.93252 -0.76519 -0.51528 -0.20976 0.118389 0.433766 0.702332 0.895105 0.991284 0.980487 0.863881 0.654049 0.373635 0.0529 -0.27354 -0.57047 -0.80583 -0.95423 -0.99965 -0.9372 -0.77361 -0.52653 -0.22264 0.105287 0.421848 0.692885 0.889149 0.989461 0.982994 0.870447 0.663966 0.385833 0.066062 -0.26084 -0.55959 -0.79795 -0.9502 -0.99991 -0.94172 -0.7819 -0.5377 -0.23547 0.092166 0.409857 0.683318 0.883038 0.987465 0.98533 0.876862 0.673767 0.397963 0.079212 -0.24809 -0.54861 -0.78994 -0.94601 -1 -0.94607 -0.79005 -0.54877 -0.24826 0.079029 0.397795 0.673632 0.876774 0.985298 0.987494 0.883124 0.683452 0.410024 0.092349 -0.23529 -0.53754 -0.78178 -0.94166 -0.99991 -0.95026 -0.79806 -0.55974 -0.26101 0.065879 0.385663 0.663829 0.870357 0.98296 0.989487 0.889233 0.693017 0.422014 0.10547 -0.22246 -0.52638 -0.77349 -0.93714 -0.99965 -0.95429 -0.80594 -0.57062 -0.27372 0.052717 0.373465 0.65391 0.863789 0.980451 0.991308 0.895187 0.702462 0.433931 0.118572 -0.20958 -0.51512 -0.76507 -0.93245 -0.99921 -0.95814 -0.81367 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-0.97777 -0.85707 -0.64388 -0.3612 -0.03955 0.286378 0.581397 0.813674 0.958143 0.999214 0.932455 0.765069 1.11542 Animat e t he wave by clicking and holding on t he end of t he slider bar 1.573716 1.876315 1.9935 The idea of using a slider for animation is from Michael J. 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