Interferencia De Ondas

Ahora veremos cómo se afecta la onda senoidal cuando se sumas dos ondas

C) Dos ondas senoidales diferentes en amplitud, longitud y desfase que dan por resultado interferencias c

Introduce los siguientes datos:

Onda f1(x): amplitud 1, periodo 1 y un desfasamiento de 0 (C = 0)

Onda f2(x): amplitud 0.5, periodo 1.5 y un desfasamiento de 180 (C = π)

7. ¿Qué valor tiene la cresta donde la interferencia es constructiva? 8. ¿Qué valor tiene la cresta donde la interferencia es destructiva? 9. ¿Cómo son la crestas respecto a las de las funciones iniciales? 10. ¿En qué momento podemos decir que la onda se repite?

Observa lo que sucede con f1(x), f2(x) y f1(x) + f2(x)

Recuerda que el periodo se relaciona con B mediante la siguiente ecuación:

T = Periodo

π = 3.1416

Introduce los valores de B con dos décimales.

Superposición de ondas

f(x) = A sen (Bx + C) + D

B1

6.2832

B2

4.1888

f1(x) = A sen (Bx + C) + D

f2(x) = A sen (Bx + C) + D

A1

B1

1

6.2832

A2

B2

0.5

4.1888

x

0

1.5 0.03

1 0.06

0.09

0.5 0.12

0.15

f1(x) = A sen (Bx + C) + D

f1(x) + f2(x) -3.67321E-06 0.124711341 0.243776586 0.35176181 0.44366782

f1(x) = A sen (Bx + C) + D f2(x) = A sen (Bx + C) + D

0 0.187381748 0.368125372 0.535827911 0.684548391 0.80901829

-3.67321E-06 -0.062670407 -0.124348786 -0.184066101 -0.240880571

0

-0.5 0.21 0.968583928 -0.385259618

f1(x) = A sen (Bx + C) + D

-0.293896192  0.515122098

0.18

0.904828179   -0.342276873

0.562551305 0.58332431

012345

-0.2

o

-0.5

0.36

0.39

0.42

0.45

0.48 1.5

0.51

0.54 1

0.57 0.5

0.6

-0.2 -0.4 -0.6

0.24 -1 0.27

-1.5 0.3 0.33

0.99802695 0.992114204 0.951055154 0.876304344

-0.422166561 -0.452415653 -0.475529847 -0.491144616

0.575860389 0.539698551 0.475525307 0.385159728

0.309010706 -0.475526442 -0.166515736 0.125326237 -0.452410961 -0.327084725

-0.062797998 -0.422160656 -0.484958654

-0.248697572 -0.385252594 -0.633950166 -0.425786869 -0.34226884 -0.76805571

-0.587792384 -0.293887277 -0.881679661

-0.929780218 -0.124338113 -1.05411833 -0.982289233 -0.062659474 -1.044948707

-1 7.34641E-06 -0.999992654

2

-0.491142552 -0.009394285

0.770509871 0.637419575 0.481748266

-0.499013706 0.271496166 -0.499013014 0.138406561

f1(x) + f2(x)

0.63

-0.728974964   -0.240870914  -0.969845878

0 -0.5

01234

0.66

-0.844333122

-0.184055856

-1.028388977

0.69

0.72 -1

0.75

-1.5

-2

-0.982285103 -0.929772105 -0.844321312 -0.728959877 -0.587774554 -0.425766928 -0.248676225 -0.062776002 0.125348102 0.309031667

0.062674051 0.124352344 0.184069517 0.24088379 0.293899164 0.342279551 0.38526196 0.422168529 0.452417217 0.475530982

-0.919611052 -0.805419761 -0.660251796 -0.488076087 -0.29387539 -0.083487377 0.136585735 0.359392527 0.577765319 0.784562649

0.78 0.81 0.84 0.87 0.9 0.93 0.96 0.99 1.02 1.05 1.08 1.11 1.14 1.17 1.2 1.23 1.26 1.29 1.32 1.35 1.38 1.41 1.44 1.47 1.5 1.53 1.56 1.59 1.62 1.65

0.684532325 0.368104881

-0.684564457 -0.809031244

0.240867695 0.124334555

-0.240887009 -0.293902135

0.925400021 0.492439435

-0.925451465 -1.102933379

2 1.5 1 0.5 0

-0.5 -1 -1.5 -2

0.904818795

0.342266163

1.247084957

0.481767579 0.491145305 0.972912884 0.637436556 0.499013936 1.136450492

0.770523919 0.499012783 1.269536702 0.876314962 0.491141863 1.367456825

0.951061965 0.475525307 1.426587271 0.992116966 0.452409397 1.444526363

0.998025566 0.422158688 1.420184254 0.968578447 0.385250253 1.3538287

01234

0.809005335

0.293884305

1.102889641

0.535809303 0.18405244 0.719861743

0.187360099 0.06265583 0.250015928 -2.20392E-05 -1.10196E-05 -3.30588E-05

-0.187403396 -0.062677695 -0.250081092 -0.368145864 -0.124355902 -0.492501765

-0.53584652

-0.184072932

-0.719919452



1.68 -0.904837562 1.71 -0.968589409 1.74 -0.998028333 1.77 -0.992111442

1.8 -0.951048343 1.83 -0.876293726 1.86 -0.770495823 1.89 -0.637402593 1.92 -0.481728953 1.95 -0.308989746 1.98 -0.125304371 2.01 0.062819994 2.04 0.248718919 2.07 0.425806811 2.1 0.587810214 2.13 0.72899005 2.16 0.84434493 2.19 0.929788331 2.22 0.982293362 2.25 0.999999999 2.28 0.982280973 2.31 0.929763991 2.34 0.844309503 2.37 0.72894479 2.4 0.587756724 2.43 0.425746986 2.46 0.248654878 2.49 0.062754007 2.52 -0.125369967 2.55 -0.309052627 2.58 -0.481786892 2.61 -0.637453537 2.64 -0.770537967 2.67 -0.876325578

2.7 -0.951068774 2.73 -0.992119728 2.76 -0.998024181 2.79 -0.968572966 2.82 -0.90480941 2.85 -0.80899238 2.88 -0.684516259 2.91 -0.535790694 2.94 -0.368084389 2.97 -0.18733845

3 4.40785E-05 3.03 0.187425045 3.06 0.368166355 3.09 0.535865128 3.12 0.684580522

-0.342282228 -0.385264301 -0.422170497 -0.452418781 -0.475532117 -0.491145993 -0.499014167 -0.499012552 -0.491141175 -0.475524172 -0.452407833 -0.42215672 -0.385247911 -0.342263485 -0.293881334 -0.240864477 -0.184049025 -0.124330997 -0.062652186 1.46928E-05 0.062681339 0.124359459 0.184076347 0.240890227 0.293905107 0.342284906 0.385266642 0.422172465 0.452420345 0.475533252 0.491146681 0.499014397 0.499012321 0.491140486 0.475523036 0.452406269 0.422154751 0.38524557 0.342260807 0.293878362 0.240861258 0.18404561 0.124327439 0.062648541 -1.8366E-05 -0.062684984 -0.124363017 -0.184079762 -0.240893446

-1.247119791 -1.35385371 -1.42019883 -1.444530223 -1.426580461 -1.367439719 -1.269509989 -1.136415145 -0.972870128 -0.784513917 -0.577712204 -0.359336726 -0.136528993 0.083543326 0.293928881 0.488125574 0.660295905 0.805457334 0.919641177 1.000014692 1.044962312 1.05412345 1.02838585 0.969835017 0.881661831 0.768031892 0.633921521 0.484926472 0.327050378 0.166480625 0.009359789 -0.13843914 -0.271525646 -0.385185092 -0.475545738 -0.539713459 -0.57586943 -0.583327396 -0.562548603 -0.515114019 -0.443655001 -0.351745085 -0.24375695 -0.124689908 2.57124E-05 0.124740061 0.243803338 0.351785365 0.443687076

3.15 0.809044198 3.18 0.904846945 3.21 0.968594889 3.24 0.998029716 3.27 0.992108678

3.3 0.951041532 3.33 0.876283108 3.36 0.770481774 3.39 0.637385611 3.42 0.48170964 3.45 0.308968785 3.48 0.125282506 3.51 -0.062841989 3.54 -0.248740265 3.57 -0.425826752

3.6 -0.587828044 3.63 -0.729005137 3.66 -0.844356739 3.69 -0.929796443 3.72 -0.982297491 3.75 -0.999999998 3.78 -0.982276842 3.81 -0.929755877 3.84 -0.844297693 3.87 -0.728929702

3.9 -0.587738893 3.93 -0.425727044 3.96 -0.248633531 3.99 -0.062732011 4.02 0.125391833 4.05 0.309073587 4.08 0.481806205 4.11 0.637470518 4.14 0.770552015 4.17 0.876336195 4.2 0.951075584 4.23 0.992122489 4.26 0.998022796 4.29 0.968567484 4.32 0.904800025 4.35 0.808979425 4.38 0.684500192 4.41 0.535772085 4.44 0.368063897 4.47 0.187316801 4.5 -6.61177E-05 4.53 -0.187446694 4.56 -0.368186846 4.59 -0.535883735

0.515136119 0.562559362 0.583325906 0.575855283 0.53968677 0.475507145 0.385135739 0.271467146

-0.293908079

-0.342287584

-0.385268984

-0.422174433

-0.452421909

-0.475534387

-0.491147369

-0.499014628

-0.499012091 0.13837352

-0.491139798 -0.475521901 -0.452404705 -0.422152783 -0.385243228 -0.342258129 -0.29387539 -0.240858039 -0.184042194 -0.124323881 -0.062644897 2.20392E-05 0.062688628 0.124366575 0.184083178 0.240896665 0.29391105 0.342290261 0.385271325 0.422176401 0.452423473 0.475535522 0.491148057 0.499014858 0.49901186 0.49113911 0.475520766 0.452403141 0.422150815 0.385240887 0.342255452 0.293872418 0.24085482 0.184038779 0.124320323 0.062641253 -2.57124E-05 -0.062692272 -0.124370133 -0.184086593

-0.009430158 -0.166553117 -0.327122199 -0.484994772 -0.633983494 -0.768084882 -0.881703434 -0.969863175 -1.028398933 -1.054120324 -1.044942388 -0.999977959 -0.919588214 -0.805389302 -0.660214515 -0.488033037 -0.293827843 -0.083436782 0.136637794 0.359444391 0.577815305 0.784609109 0.972954262 1.136485376 1.269563875 1.367475305 1.42659635 1.44452563 1.420173611 1.353808371 1.247055477 1.102851843 0.925355012 0.719810864 0.49238422 0.249958053 -9.18301E-05 -0.250138966 -0.492556979 -0.719970328

4.62 -0.684596587 4.65 -0.809057151 4.68 -0.904856328 4.71 -0.968600369 4.74 -0.998031099 4.77 -0.992105915 4.8 -0.95103472 4.83 -0.87627249 4.86 -0.770467724 4.89 -0.637368628 4.92 -0.481690326 4.95 -0.308947824 4.98 -0.12526064 5.01 0.062863985 5.04 0.248761612 5.07 0.425846693 5.1 0.587845873 5.13 0.729020223 5.16 0.844368547 5.19 0.929804555 5.22 0.982301619 5.25 0.999999997 5.28 0.982272711 5.31 0.929747762 5.34 0.844285882 5.37 0.728914614 5.4 0.587721062 5.43 0.425707101 5.46 0.248612184 5.49 0.062710015 5.52 -0.125413698 5.55 -0.309094547 5.58 -0.481825517 5.61 -0.637487498 5.64 -0.770566062 5.67 -0.876346811

5.7 -0.951082393

...