{"id":463,"date":"2023-06-16T22:17:21","date_gmt":"2023-06-16T22:17:21","guid":{"rendered":"https:\/\/physigeek.com\/pt\/onda-harmonica\/"},"modified":"2023-06-16T22:17:21","modified_gmt":"2023-06-16T22:17:21","slug":"onda-harmonica","status":"publish","type":"post","link":"https:\/\/physigeek.com\/pt\/onda-harmonica\/","title":{"rendered":"Onda harm\u00f4nica"},"content":{"rendered":"<p>Este artigo explica o que s\u00e3o ondas harm\u00f4nicas na f\u00edsica e quais s\u00e3o suas caracter\u00edsticas. Voc\u00ea tamb\u00e9m encontrar\u00e1 exemplos de ondas harm\u00f4nicas e qual \u00e9 a equa\u00e7\u00e3o de uma onda harm\u00f4nica. Al\u00e9m disso, voc\u00ea poder\u00e1 ver a rela\u00e7\u00e3o entre as ondas harm\u00f4nicas e outros conceitos f\u00edsicos. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%C2%BFQue-es-una-onda-armonica\"><\/span> O que \u00e9 uma onda harm\u00f4nica?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Ondas harm\u00f4nicas s\u00e3o ondas que oscilam cont\u00ednua e periodicamente, ou seja, o gr\u00e1fico de uma onda harm\u00f4nica se repete a cada intervalo de tempo fixo. Portanto, uma onda harm\u00f4nica \u00e9 definida por uma fun\u00e7\u00e3o seno ou cosseno.<\/p>\n<p> Por exemplo, a onda gerada pela vibra\u00e7\u00e3o de uma corda \u00e9 uma onda harm\u00f4nica, pois a corda oscila verticalmente periodicamente. Al\u00e9m disso, a onda harm\u00f4nica gerada pode ser descrita por uma fun\u00e7\u00e3o senoidal. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Caracteristicas-de-las-ondas-armonicas\"><\/span> Caracter\u00edsticas das ondas harm\u00f4nicas<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> As ondas harm\u00f4nicas possuem as seguintes caracter\u00edsticas ou partes:<\/p>\n<ul style=\"color:#4fd12f; font-weight: bold;\">\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>Alongamento (y)<\/strong> : \u00e9 a dist\u00e2ncia entre a posi\u00e7\u00e3o da onda e sua posi\u00e7\u00e3o de equil\u00edbrio.<\/span><\/li>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>Amplitude (A)<\/strong> : \u00e9 a dist\u00e2ncia entre a extens\u00e3o m\u00e1xima e sua posi\u00e7\u00e3o de equil\u00edbrio.<\/span><\/li>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>Crista<\/strong> : cada um dos pontos mais altos da onda.<\/span><\/li>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>Vale<\/strong> : cada um dos pontos mais baixos da onda.<\/span><\/li>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>Ciclo ou oscila\u00e7\u00e3o<\/strong> : \u00e9 o caminho da onda de um ponto ao pr\u00f3ximo ponto equivalente.<\/span><\/li>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>Comprimento de onda (\u03bb)<\/strong> : \u00e9 a dist\u00e2ncia que separa dois pontos equivalentes consecutivos da onda.<\/span><\/li>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>Per\u00edodo (T)<\/strong> : \u00e9 o tempo necess\u00e1rio para completar uma oscila\u00e7\u00e3o completa.<\/span><\/li>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>Frequ\u00eancia (f)<\/strong> : \u00e9 o n\u00famero de oscila\u00e7\u00f5es ou vibra\u00e7\u00f5es que a onda faz por unidade de tempo.<\/span><\/li>\n<p style=\"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-531bea341cf9b96ec2c355cc9e57d511_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f=\\cfrac{1}{T}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"49\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>Frequ\u00eancia angular (ou pulsa\u00e7\u00e3o) (\u03c9)<\/strong> : \u00e9 a velocidade com que a onda oscila.<\/span><\/li>\n<p style=\"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-df8b803de06998e6a4ef5082a65705b7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\omega=\\cfrac{2\\cdot \\pi}{T}=2\\cdot \\pi \\cdot f\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"149\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>N\u00famero de onda (k)<\/strong> : \u00c9 definido como o n\u00famero de ciclos realizados ao longo de um comprimento de 2\u03c0 metros.<\/span><\/li>\n<p style=\"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-20c1803a9dcde209173b7c67b98b2251_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"k=\\cfrac{2\\cdot \\pi}{\\lambda}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"68\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>Velocidade de propaga\u00e7\u00e3o (v)<\/strong> : \u00e9 a velocidade com que a onda se propaga.<\/span> <\/li>\n<p style=\"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-85a8e2ee07d189b4d6fb7a95d6ee598c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"v=\\cfrac{\\lambda}{T}=\\cfrac{\\omega}{k}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"85\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<\/ul>\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\/caracteristiques-des-ondes-transversales.png\" alt=\"caracter\u00edsticas de uma onda harm\u00f4nica, partes de uma onda harm\u00f4nica\" class=\"wp-image-9217\" width=\"717\" height=\"369\" srcset=\"https:\/\/physigeek.com\/wp-content\/uploads\/2023\/09\/caracteristiques-des-ondes-transversales-300x155.png 300w, https:\/\/physigeek.com\/wp-content\/uploads\/2023\/09\/caracteristiques-des-ondes-transversales-1024x528.png 1024w, https:\/\/physigeek.com\/wp-content\/uploads\/2023\/09\/caracteristiques-des-ondes-transversales-768x396.png 768w, https:\/\/physigeek.com\/wp-content\/uploads\/2023\/09\/caracteristiques-des-ondes-transversales.png 1368w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\"><\/figure>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Ejemplos-de-ondas-armonicas\"><\/span> Exemplos de ondas harm\u00f4nicas<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Depois de vermos a defini\u00e7\u00e3o de onda harm\u00f4nica e quais s\u00e3o suas caracter\u00edsticas, veremos v\u00e1rios exemplos deste tipo de ondas para finalizar a assimila\u00e7\u00e3o do conceito.<\/p>\n<p> <u style=\"text-decoration-color:#4fd12f\"><strong>Exemplos de ondas harm\u00f4nicas:<\/strong><\/u><\/p>\n<ul style=\"color:#4fd12f; font-weight: bold;\">\n<li style=\"margin-bottom:15px\"> <span style=\"color:#101010;font-weight: normal;\">As ondas sonoras s\u00e3o ondas harm\u00f4nicas.<\/span><\/li>\n<li style=\"margin-bottom:15px\"> <span style=\"color:#101010;font-weight: normal;\">A onda produzida quando uma corda vibra.<\/span><\/li>\n<li style=\"margin-bottom:15px\"> <span style=\"color:#101010;font-weight: normal;\">As ondas que surgem na superf\u00edcie de uma po\u00e7a quando uma pedra \u00e9 atirada.<\/span><\/li>\n<li style=\"margin-bottom:15px\"> <span style=\"color:#101010;font-weight: normal;\">Ondas geradas por <a href=\"https:\/\/physigeek.com\/pt\">movimentos harm\u00f4nicos simples<\/a> .<\/span> <\/li>\n<\/ul>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Formula-de-una-onda-armonica\"><\/span> F\u00f3rmula de uma onda harm\u00f4nica<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>A equa\u00e7\u00e3o da onda harm\u00f4nica \u00e9 y(x,t) = A sin(k x \u00b1 \u03c9 t + \u03c6 <sub>0<\/sub> ).<\/strong> Esta f\u00f3rmula \u00e9 usada para calcular o alongamento de um ponto na onda harm\u00f4nica em uma posi\u00e7\u00e3o espec\u00edfica e em um momento espec\u00edfico.<\/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-5bf20982fc10ac516d8272178ef0935c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y(x,t)=A\\cdot \\text{sin}(k\\cdot x\\pm w\\cdot t+\\phi_0)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"259\" style=\"vertical-align: -5px;\"><\/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 da 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-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 da onda harm\u00f4nica. <\/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-7e5fbfa0bbbd9f3051cd156a0f1b5e31_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u00e9 a dist\u00e2ncia do ponto estudado at\u00e9 a origem da 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-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 da 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 de 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-c8618f3820889d0002a7eefeeb2aaf41_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\phi_0\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"18\" style=\"vertical-align: -4px;\"><\/p>\n<p> \u00e9 a fase inicial da onda.<\/span><\/li>\n<\/ul>\n<p> <strong>Nota:<\/strong> Tenha em mente que existem diversas maneiras de expressar a equa\u00e7\u00e3o de uma onda harm\u00f4nica, portanto ela tamb\u00e9m pode ser expressa por uma fun\u00e7\u00e3o cosseno. Por\u00e9m, a express\u00e3o mais utilizada \u00e9 a fun\u00e7\u00e3o explicada neste artigo.<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Fase-de-una-onda-armonica\"><\/span>Fase de uma onda harm\u00f4nica<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> A <strong>fase (ou \u00e2ngulo de fase) de uma onda harm\u00f4nica<\/strong> \u00e9 o estado de vibra\u00e7\u00e3o de um ponto na onda. Simplificando, a fase de uma onda harm\u00f4nica indica onde est\u00e1 um ponto espec\u00edfico no ciclo da onda.<\/p>\n<p> A fase de uma onda \u00e9 expressa em radianos (rad) ou graus (\u00ba). A diferen\u00e7a de fase entre dois pontos equivalentes \u00e9, portanto, 2\u03c0 rad ou 360\u00ba.<\/p>\n<p> Al\u00e9m disso, a fase inicial de uma onda determina em que situa\u00e7\u00e3o se encontra o estado vibracional inicial de uma onda. Assim, dependendo do valor da fase inicial, o valor do alongamento inicial da onda ser\u00e1 um ou outro. Por exemplo, se definirmos uma onda harm\u00f4nica usando uma fun\u00e7\u00e3o senoidal e a fase inicial for zero, isso significa que o alongamento da onda ser\u00e1 y=0 no in\u00edcio.<\/p>\n<p> A fase das ondas harm\u00f4nicas tamb\u00e9m \u00e9 usada para comparar o estado de vibra\u00e7\u00e3o de duas ondas harm\u00f4nicas diferentes. Assim, voc\u00ea deve conhecer dois conceitos ligados \u00e0s fases das ondas harm\u00f4nicas:<\/p>\n<ul style=\"color:#4fd12f; font-weight: bold;\">\n<li style=\"margin-bottom:20px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>Duas ondas harm\u00f4nicas est\u00e3o em fase<\/strong> quando possuem o mesmo estado de vibra\u00e7\u00e3o, ou seja, possuem um deslocamento de fase de 0\u00ba (ou 0 rad). Neste caso, os pontos equivalentes das duas ondas ocorrem ao mesmo tempo, por exemplo, as cristas e vales das ondas ocorrem simultaneamente.<\/span><\/li>\n<li style=\"margin-bottom:20px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>Duas ondas harm\u00f4nicas est\u00e3o em antifase<\/strong> quando seu estado de vibra\u00e7\u00e3o \u00e9 oposto, portanto est\u00e3o 180\u00ba fora de fase (ou \u03c0 rad). Por exemplo, se duas ondas harm\u00f4nicas estiverem em antifase, as cristas de uma onda ocorrer\u00e3o quando ocorrerem as depress\u00f5es da outra onda.<\/span> <\/li>\n<\/ul>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Onda-armonica-y-onda-estacionaria\"><\/span> Onda harm\u00f4nica e onda estacion\u00e1ria<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Por fim, veremos qual a diferen\u00e7a entre uma onda harm\u00f4nica e uma onda estacion\u00e1ria, pois s\u00e3o dois tipos de ondas frequentemente confundidas na f\u00edsica.<\/p>\n<p> Uma <strong>onda estacion\u00e1ria<\/strong> \u00e9 uma perturba\u00e7\u00e3o oscilat\u00f3ria cujos picos oscilam verticalmente, mas n\u00e3o avan\u00e7am longitudinalmente. Al\u00e9m disso, as ondas estacion\u00e1rias s\u00e3o o resultado da interfer\u00eancia entre duas ondas com as mesmas caracter\u00edsticas, mas avan\u00e7ando na dire\u00e7\u00e3o oposta, ou seja, as ondas estacion\u00e1rias s\u00e3o produzidas quando duas ondas harm\u00f4nicas semelhantes, mas com uma dire\u00e7\u00e3o de propaga\u00e7\u00e3o oposta, se sobrep\u00f5em.<\/p>\n<p> Portanto, <strong>a principal diferen\u00e7a entre uma onda harm\u00f4nica e uma onda estacion\u00e1ria<\/strong> \u00e9 que uma onda harm\u00f4nica se propaga longitudinalmente, enquanto uma onda estacion\u00e1ria oscila verticalmente, mas n\u00e3o avan\u00e7a longitudinalmente. Al\u00e9m disso, as ondas estacion\u00e1rias s\u00e3o formadas pela superposi\u00e7\u00e3o de duas ondas harm\u00f4nicas. <\/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 \u00e9 uma onda estacion\u00e1ria?<\/a><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Este artigo explica o que s\u00e3o ondas harm\u00f4nicas na f\u00edsica e quais s\u00e3o suas caracter\u00edsticas. Voc\u00ea tamb\u00e9m encontrar\u00e1 exemplos de ondas harm\u00f4nicas e qual \u00e9 a equa\u00e7\u00e3o de uma onda harm\u00f4nica. Al\u00e9m disso, voc\u00ea poder\u00e1 ver a rela\u00e7\u00e3o entre as ondas harm\u00f4nicas e outros conceitos f\u00edsicos. O que \u00e9 uma onda harm\u00f4nica? Ondas harm\u00f4nicas s\u00e3o &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/physigeek.com\/pt\/onda-harmonica\/\"> <span class=\"screen-reader-text\">Onda harm\u00f4nica<\/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-463","post","type-post","status-publish","format-standard","hentry","category-cinematografico"],"yoast_head":"<!-- This site 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