{"id":459,"date":"2023-06-17T02:27:16","date_gmt":"2023-06-17T02:27:16","guid":{"rendered":"https:\/\/physigeek.com\/pt\/fisica-de-interferencia-de-ondas\/"},"modified":"2023-06-17T02:27:16","modified_gmt":"2023-06-17T02:27:16","slug":"fisica-de-interferencia-de-ondas","status":"publish","type":"post","link":"https:\/\/physigeek.com\/pt\/fisica-de-interferencia-de-ondas\/","title":{"rendered":"Interfer\u00eancia de onda (f\u00edsica)"},"content":{"rendered":"<p>Este artigo explica o que \u00e9 interfer\u00eancia de ondas na f\u00edsica. Assim, voc\u00ea aprender\u00e1 o que significa a interfer\u00eancia de duas ondas, os tipos de interfer\u00eancia de ondas, exemplos de interfer\u00eancia de ondas e, por fim, a f\u00f3rmula que descreve a interfer\u00eancia de duas ondas. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%C2%BFQue-es-la-interferencia-de-ondas\"><\/span> O que \u00e9 interfer\u00eancia de ondas?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Na f\u00edsica, <strong>a interfer\u00eancia de ondas<\/strong> \u00e9 um fen\u00f4meno que ocorre quando duas ou mais ondas se cruzam. Em outras palavras, a interfer\u00eancia de ondas consiste na superposi\u00e7\u00e3o de duas ou mais ondas para formar uma nova onda.<\/p>\n<p> Assim, a onda resultante da interfer\u00eancia de duas ondas \u00e9 a soma das ondas originais. Assim, para obter a equa\u00e7\u00e3o de duas ondas interferentes, basta somar suas respectivas equa\u00e7\u00f5es. A seguir veremos qual \u00e9 a equa\u00e7\u00e3o para a interfer\u00eancia de duas ondas.<\/p>\n<p> Por exemplo, se atirarmos duas pedras num lago cheio de \u00e1gua, o impacto de cada pedra ir\u00e1 gerar uma onda que se propagar\u00e1 atrav\u00e9s da \u00e1gua. Ent\u00e3o as duas ondas geradas se cruzar\u00e3o e ocorrer\u00e1 a interfer\u00eancia das duas ondas, de modo que ser\u00e1 criada uma onda resultante da soma das duas ondas originais.<\/p>\n<p> Tenha em mente que a interfer\u00eancia \u00e9 um fen\u00f4meno f\u00edsico que pode ocorrer com todos os tipos de ondas: ondas de luz, ondas de r\u00e1dio, ondas sonoras, etc. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Tipos-de-interferencia-de-ondas\"><\/span> Tipos de interfer\u00eancia de ondas<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Na f\u00edsica, existem dois <strong>tipos de interfer\u00eancia de ondas<\/strong> :<\/p>\n<ul style=\"color:#4fd12f; font-weight: bold;\">\n<li style=\"margin-bottom:18px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>Interfer\u00eancia de onda construtiva<\/strong> \u2013 Um tipo de interfer\u00eancia de onda que ocorre quando ondas sobrepostas est\u00e3o em fase.<\/span><\/li>\n<li style=\"margin-bottom:18px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>Interfer\u00eancia de onda destrutiva<\/strong> \u2013 Um tipo de interfer\u00eancia de onda que ocorre quando as ondas que se cruzam est\u00e3o em antifase.<\/span><\/li>\n<\/ul>\n<p> Cada tipo de interfer\u00eancia de onda \u00e9 explicado em detalhes abaixo. <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Interferencia-de-ondas-constructiva\"><\/span> Interfer\u00eancia de onda construtiva<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> <strong>A interfer\u00eancia de onda construtiva<\/strong> ocorre quando duas ou mais ondas com a mesma frequ\u00eancia e em fase se sobrep\u00f5em. Portanto, a onda resultante da interfer\u00eancia construtiva de duas ondas \u00e9 uma onda de maior amplitude. <\/p>\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/uploads\/2023\/09\/interference-onde-constructive.png\" alt=\"interfer\u00eancia de onda construtiva\" class=\"wp-image-9275\" width=\"477\" height=\"321\" srcset=\"https:\/\/physigeek.com\/wp-content\/uploads\/2023\/09\/interference-onde-constructive-300x202.png 300w, https:\/\/physigeek.com\/wp-content\/uploads\/2023\/09\/interference-onde-constructive-1024x690.png 1024w, https:\/\/physigeek.com\/wp-content\/uploads\/2023\/09\/interference-onde-constructive-768x518.png 768w, https:\/\/physigeek.com\/wp-content\/uploads\/2023\/09\/interference-onde-constructive.png 1102w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\"><\/figure>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Interferencia-de-ondas-destructiva\"><\/span> Interfer\u00eancia de ondas destrutivas<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> <strong>A interfer\u00eancia de onda destrutiva<\/strong> ocorre quando duas ou mais ondas antif\u00e1sicas (180\u00b0 fora de fase) com a mesma frequ\u00eancia se sobrep\u00f5em. Portanto, a onda resultante da interfer\u00eancia destrutiva \u00e9 uma onda de menor amplitude; \u00e0s vezes, durante interfer\u00eancias destrutivas, as ondas se cancelam. <\/p>\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/uploads\/2023\/09\/interference-onde-destructrice.png\" alt=\"interfer\u00eancia de onda destrutiva\" class=\"wp-image-9278\" width=\"478\" height=\"205\" srcset=\"https:\/\/physigeek.com\/wp-content\/uploads\/2023\/09\/interference-onde-destructrice-300x129.png 300w, https:\/\/physigeek.com\/wp-content\/uploads\/2023\/09\/interference-onde-destructrice-1024x440.png 1024w, https:\/\/physigeek.com\/wp-content\/uploads\/2023\/09\/interference-onde-destructrice-768x330.png 768w, https:\/\/physigeek.com\/wp-content\/uploads\/2023\/09\/interference-onde-destructrice.png 1104w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\"><\/figure>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Ejemplos-de-interferencias-de-ondas\"><\/span> Exemplos de interfer\u00eancia de ondas<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Depois de vermos a defini\u00e7\u00e3o de interfer\u00eancia de ondas e quais s\u00e3o os diferentes tipos de interfer\u00eancia de ondas, veremos exemplos desse fen\u00f4meno f\u00edsico para compreender completamente o conceito.<\/p>\n<p> Abaixo voc\u00ea pode ver dois exemplos de ondas interferentes. No primeiro exemplo, as ondas se cancelam, portanto \u00e9 uma interfer\u00eancia de onda destrutiva. Enquanto no segundo exemplo as ondas geram uma onda de maior amplitude e, portanto, a interfer\u00eancia das ondas \u00e9 construtiva. <\/p>\n<figure class=\"wp-block-image aligncenter size-full\"><img decoding=\"async\" loading=\"lazy\" width=\"360\" height=\"223\" src=\"https:\/\/physigeek.com\/wp-content\/uploads\/2023\/09\/exemples-dinterferences-dondes.gif\" alt=\"exemplos de interfer\u00eancia de ondas (f\u00edsica)\" class=\"wp-image-9281\"><\/figure>\n<p> Observe que ap\u00f3s o fen\u00f4meno de interfer\u00eancia das ondas, as ondas iniciais mant\u00eam sua forma original e continuam a se propagar em sua dire\u00e7\u00e3o.<\/p>\n<p> Na f\u00edsica, o <strong>princ\u00edpio da superposi\u00e7\u00e3o de ondas<\/strong> afirma que a onda resultante da interfer\u00eancia entre duas ou mais ondas \u00e9 a soma de cada uma das ondas separadamente. Como voc\u00ea pode ver na figura acima, quando duas ondas passam uma pela outra, elas se sobrep\u00f5em e d\u00e3o origem a uma nova onda resultante que \u00e9 a soma das ondas originais.<\/p>\n<p> Finalmente, deve-se notar que as ondas estacion\u00e1rias tamb\u00e9m s\u00e3o um exemplo de interfer\u00eancia de duas ondas. Na verdade, as ondas estacion\u00e1rias s\u00e3o um tipo de onda estudada na f\u00edsica porque possuem caracter\u00edsticas muito particulares porque prov\u00eam da interfer\u00eancia de duas ondas. <\/p>\n<div style=\"background-color:#FFFDE7; padding-top: 10px; padding-bottom: 10px; padding-right: 10px; padding-left: 20px; border: 2.5px dashed #FFB74D; border-radius:20px;\"> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>Veja:<\/strong> <a href=\"https:\/\/physigeek.com\/pt\/onda-parada\/\">O que s\u00e3o ondas estacion\u00e1rias?<\/a> <\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Formula-de-la-interferencia-de-ondas\"><\/span> F\u00f3rmula de interfer\u00eancia de ondas<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> A f\u00f3rmula da interfer\u00eancia de duas ondas \u00e9 dada pela soma das equa\u00e7\u00f5es das duas ondas iniciais. <strong>Assim, a equa\u00e7\u00e3o para a interfer\u00eancia de duas ondas \u00e9 y=2 A sin[k (x <sub>1<\/sub> +x <sub>2<\/sub> )\/2-\u03c9 t+\u03c6\/2] cos[k (x <sub>1<\/sub> -x <sub>2<\/sub> )\/2- \u03c6\/ 2]<\/strong> .<\/p>\n<p class=\"has-text-align-center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-d9125d78ba28773d8a8e0a1a0da8230e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle y=2\\cdot A\\cdot \\text{sin}\\left(\\frac{k(x_1+x_2)}{2}-\\omega\\cdot t+\\frac{\\phi}{2}\\ droite)\\text{cos}\\left(\\frac{k(x_1-x_2)}{2}-\\frac{\\phi}{2}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"522\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p style=\"margin-bottom:5px\"> Ouro: <\/p>\n<ul style=\"color:#4fd12f; font-weight: bold;\">\n<li style=\"margin-bottom:5px\"><span style=\"color:#101010;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-38461fc041e953482219abf5d4cce1cb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\"><\/p>\n<p> \u00e9 o alongamento do ponto estudado. <\/span><\/li>\n<li style=\"margin-bottom:5px\"><span style=\"color:#101010;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-816b613a4f79d4bf9cb51396a9654120_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"13\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u00e9 a amplitude das ondas originais. <\/span><\/li>\n<li style=\"margin-bottom:5px\"><span style=\"color:#101010;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-d42bc2203d6f76ad01b27ac9acc0bee1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"k\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u00e9 o n\u00famero de onda. <\/span><\/li>\n<li style=\"margin-bottom:5px\"><span style=\"color:#101010;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-11e46ba8b122ff2ec557030bd2f06155_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x_1,x_2\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"43\" style=\"vertical-align: -4px;\"><\/p>\n<p> \u00e9 a dist\u00e2ncia entre o ponto de estudo e o foco da onda 1 e da onda 2, respectivamente. <\/span><\/li>\n<li style=\"margin-bottom:5px\"><span style=\"color:#101010;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-fbffdce91996e0a17795d82e8e6996d9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\omega\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u00e9 a frequ\u00eancia angular ou pulsa\u00e7\u00e3o. <\/span><\/li>\n<li style=\"margin-bottom:5px\"><span style=\"color:#101010;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-fd9cb27edab3f0a8a249bc80cc9c6ee2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"t\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"6\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u00e9 o momento do tempo. <\/span><\/li>\n<li style=\"margin-bottom:5px\"><span style=\"color:#101010;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-8358131e7f71b02f5a1b767b67603090_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\phi\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"11\" style=\"vertical-align: -4px;\"><\/p>\n<p> \u00e9 o intervalo de tempo entre as duas ondas iniciais.<\/span><\/li>\n<\/ul>\n<p> Observe que se ambas as ondas interferentes se originam do mesmo ponto, ent\u00e3o x <sub>1<\/sub> = x <sub>2<\/sub> = x \u00e9 v\u00e1lido. Ent\u00e3o, nesse caso, a equa\u00e7\u00e3o para a interfer\u00eancia de duas ondas \u00e9 a seguinte:<\/p>\n<p class=\"has-text-align-center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-89386ad637b14c93c411c4d53c775d09_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle y=2\\cdot A\\cdot \\text{sin}\\left(k\\cdot x-\\omega\\cdot t+\\frac{\\phi}{2}\\right)\\text{cos}\\left (\\frac{\\phi}{2}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"320\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p> Lembre-se de que o n\u00famero de onda e a frequ\u00eancia angular de uma onda s\u00e3o calculados pelas seguintes f\u00f3rmulas:<\/p>\n<p class=\"has-text-align-center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-bd9a9c86ac7bfe615da6e49025b8b40f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}k=\\cfrac{2\\pi}{\\lambda}\\\\[4ex]\\omega=\\cfrac{2\\pi}{T}=2\\pi f\\end{ tableau}\" title=\"Rendered by QuickLaTeX.com\" height=\"104\" width=\"110\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p style=\"margin-bottom:5px\"> Ouro: <\/p>\n<ul style=\"color:#4fd12f; font-weight: bold;\">\n<li style=\"margin-bottom:5px\"><span style=\"color:#101010;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-d42bc2203d6f76ad01b27ac9acc0bee1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"k\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u00e9 o n\u00famero de onda. <\/span><\/li>\n<li style=\"margin-bottom:5px\"><span style=\"color:#101010;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-8c37d2f1acb1d49f3e5e655797880475_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\lambda\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"10\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u00e9 o comprimento de onda. <\/span><\/li>\n<li style=\"margin-bottom:5px\"><span style=\"color:#101010;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-fbffdce91996e0a17795d82e8e6996d9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\omega\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u00e9 a frequ\u00eancia angular ou pulsa\u00e7\u00e3o. <\/span><\/li>\n<li style=\"margin-bottom:5px\"><span style=\"color:#101010;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-7e093fd43ad2c244140c11afe4d4bdff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"T\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"13\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u00e9 o ponto. <\/span><\/li>\n<li style=\"margin-bottom:5px\"><span style=\"color:#101010;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-f5844370b6482674a233a3063f762555_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"10\" style=\"vertical-align: -4px;\"><\/p>\n<p> \u00e9 a frequ\u00eancia. <\/span><\/li>\n<\/ul>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__FFF8E1\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#FFF8E1\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>Veja demonstra\u00e7\u00e3o da equa\u00e7\u00e3o para interfer\u00eancia de duas ondas<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Dadas as equa\u00e7\u00f5es de duas ondas de propaga\u00e7\u00e3o da mesma frequ\u00eancia e mesma amplitude, mas com uma diferen\u00e7a de fase de um certo \u00e2ngulo \u03c6:<\/p>\n<p class=\"has-text-align-center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-0a41489f1ca067b0955dd725e0986cf6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}y_1=A\\cdot \\text{sin}(k\\cdot x_1-\\omega\\cdot t)\\\\[3ex]y_2=A\\cdot \\text{sin}(k \\cdot x_2-\\omega\\cdot t+\\phi )\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"64\" width=\"226\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> A onda resultante da interfer\u00eancia das duas ondas \u00e9 a soma das duas ondas oscilat\u00f3rias, portanto a equa\u00e7\u00e3o da interfer\u00eancia das duas ondas ser\u00e1 a soma alg\u00e9brica das duas equa\u00e7\u00f5es anteriores:<\/p>\n<p class=\"has-text-align-center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-3bf4f6e9cbead885e080c5275fd5b8a3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}y=y_1+y_2\\\\[3ex]y=A\\cdot \\text{sin}(k\\cdot x_1-\\omega\\cdot t)+A\\cdot \\text{ sin}(k\\cdot x_2-\\omega\\cdot t+\\phi )\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"61\" width=\"402\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Aplicaremos ent\u00e3o a seguinte f\u00f3rmula trigonom\u00e9trica:<\/p>\n<p class=\"has-text-align-center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-709f860df485f9933890e923dc1318a9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\text{sin}(A)+\\text{sin}(B)=2\\cdot \\text{sin}\\left(\\frac{A+B}{2}\\right)\\cdot\\ texte{cos}\\left(\\frac{AB}{2}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"410\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Assim, aplicando a f\u00f3rmula trigonom\u00e9trica anterior, chegamos \u00e0 equa\u00e7\u00e3o da interfer\u00eancia de duas ondas: <\/p>\n<p class=\"has-text-align-center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-59ee4b2f6559532dfa119d290e3f1b59_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}\\displaystyle y=A\\text{sin}(kx_1-\\omega t)+A\\cdot \\text{sin}(kx_2-\\omega t+\\phi)\\\\[4ex ]\\displaystyle y=2A\\text{sin}\\left(\\frac{(kx_1-\\omega t)+(kx_2-\\omega t+\\phi)}{2}\\right)\\text{cos}\\left(\\ frac{(kx_1-\\omega t)-(kx_2-\\omega t+\\phi)}{2}\\right)\\\\[4ex]\\displaystyle y=2A\\text{sin}\\left(\\frac{k(x_1 +x_2)}{2}-\\omega t+\\frac{\\phi}{2}\\right)\\text{cos}\\left(\\frac{k(x_1-x_2)}{2}-\\frac{\\phi }{2}\\right)\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"157\" width=\"636\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Este artigo explica o que \u00e9 interfer\u00eancia de ondas na f\u00edsica. Assim, voc\u00ea aprender\u00e1 o que significa a interfer\u00eancia de duas ondas, os tipos de interfer\u00eancia de ondas, exemplos de interfer\u00eancia de ondas e, por fim, a f\u00f3rmula que descreve a interfer\u00eancia de duas ondas. O que \u00e9 interfer\u00eancia de ondas? Na f\u00edsica, a interfer\u00eancia &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/physigeek.com\/pt\/fisica-de-interferencia-de-ondas\/\"> <span class=\"screen-reader-text\">Interfer\u00eancia de onda (f\u00edsica)<\/span> Leia mais &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"","footnotes":""},"categories":[3],"tags":[],"class_list":["post-459","post","type-post","status-publish","format-standard","hentry","category-cinematografico"],"yoast_head":"<!-- This site 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