{"id":2410,"date":"2016-09-11T00:18:37","date_gmt":"2016-09-11T00:18:37","guid":{"rendered":"http:\/\/fisicaevestibular.com.br\/novo\/?page_id=2410"},"modified":"2024-08-23T15:12:32","modified_gmt":"2024-08-23T15:12:32","slug":"reflexao-e-refracao-de-ondas","status":"publish","type":"page","link":"https:\/\/fisicaevestibular.com.br\/novo\/ondulatoria\/ondas\/reflexao-e-refracao-de-ondas\/","title":{"rendered":"Reflex\u00e3o e Refra\u00e7\u00e3o de Ondas"},"content":{"rendered":"

Reflex\u00e3o e Refra\u00e7\u00e3o de Ondas<\/b><\/span><\/span><\/span><\/p>\n

Reflex\u00e3o de uma onda<\/b><\/span><\/span><\/span><\/p>\n

Uma <\/b><\/span><\/span><\/span>onda sofre reflex\u00e3o <\/b><\/span><\/span><\/span>quando, <\/b><\/span><\/span><\/span>propagando-se em um dado meio<\/b><\/span><\/span><\/span>, atinge a <\/b><\/span><\/span><\/span>interface <\/b><\/span><\/span><\/span>de <\/b><\/span><\/span><\/span>separa\u00e7\u00e3o com outro meio<\/b><\/span><\/span><\/span> e, em seguida, <\/b><\/span><\/span><\/span>volta a se propagar no meio inicial.<\/b><\/span><\/span><\/span><\/p>\n

Reflex\u00e3o em meios unidimensionais<\/b><\/span><\/span><\/span><\/p>\n

A <\/b><\/span><\/span><\/span>reflex\u00e3o<\/b><\/span><\/span><\/span> de uma onda num <\/b><\/span><\/span><\/span>meio unidimensional, <\/b><\/span><\/span><\/span>como por exemplo, <\/b><\/span><\/span><\/span>numa corda, <\/b><\/span><\/span><\/span>pode ocorrer em <\/b><\/span><\/span><\/span>duas situa\u00e7\u00f5es:<\/b><\/span><\/span><\/span><\/p>\n

\"\" Extremidade fixa<\/b><\/span><\/span><\/span>\u00a0\"\"<\/b><\/span><\/span><\/span> <\/b>A <\/b><\/span><\/span><\/span>fonte (A) <\/b><\/span><\/span><\/span>provoca uma <\/b><\/span><\/span><\/span>oscila\u00e7\u00e3o completa <\/b><\/span><\/span><\/span>e a <\/b><\/span><\/span><\/span>onda se propaga com velocidade V at\u00e9 o ponto B que est\u00e1 fixo, preso<\/b><\/span><\/span><\/span>, por exemplo, a uma <\/b><\/span><\/span><\/span>parede.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Quando o <\/b><\/span><\/span><\/span>pulso chega \u00e0 B <\/b><\/span><\/span><\/span>(extremidade fixa), <\/b><\/span><\/span><\/span>cada ponto da corda aplica na parede uma for\u00e7a\u00a0 <\/b><\/span><\/span><\/span>e, pelo <\/b><\/span><\/span><\/span>princ\u00edpio da a\u00e7\u00e3o e rea\u00e7\u00e3o, <\/b><\/span><\/span><\/span>a <\/b><\/span><\/span><\/span>parede reagir\u00e1 sobre cada ponto da corda com uma for\u00e7a de mesma intensidade, mesma dire\u00e7\u00e3o mas sentido contr\u00e1rio, <\/b><\/span><\/span><\/span>produzindo um\u00a0<\/b><\/span><\/span><\/span>pulso invertido<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>ap\u00f3s a <\/b><\/span><\/span><\/span>reflex\u00e3o,<\/b><\/span><\/span><\/span> mas com a <\/b><\/span><\/span><\/span>mesma velocidade V,<\/b><\/span><\/span><\/span> <\/b>pois o <\/b><\/span><\/span><\/span>meio<\/b><\/span><\/span><\/span> (corda) \u00e9 o <\/b><\/span><\/span><\/span>mesmo.<\/b><\/span><\/span><\/span><\/p>\n

A <\/b><\/span><\/span><\/span>amplitude A<\/b><\/span><\/span><\/span> tamb\u00e9m <\/b><\/span><\/span><\/span>ser\u00e1 a mesma, supondo n\u00e3o haver perda de energia.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

\"\"\u00a0<\/span>Extremidade livre<\/b><\/span><\/span><\/span>\u00a0\"\"<\/b><\/span><\/span><\/span> <\/b>Neste caso, quando o <\/b><\/span><\/span><\/span>pulso chega em B, cada ponto da corda n\u00e3o trocar\u00e1 for\u00e7as com a parede, <\/b><\/span><\/span><\/span>pois a <\/b><\/span><\/span><\/span>argola <\/b><\/span><\/span><\/span>de <\/b><\/span><\/span><\/span>massa desprez\u00edvel e sem atrito, sobe e desce, <\/b><\/span><\/span><\/span>provocando, <\/b><\/span><\/span><\/span>ap\u00f3s a reflex\u00e3o, um pulso que retornar\u00e1\u00a0<\/b><\/span><\/span><\/span>sem invers\u00e3o de<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>fase<\/b><\/span><\/span><\/span>, <\/b><\/span><\/span><\/span>ou seja, id\u00eantico ao<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

que chega, mas com a <\/b><\/span><\/span><\/span>mesma velocidade V,<\/b><\/span><\/span><\/span> <\/b>pois o <\/b><\/span><\/span><\/span>meio<\/b><\/span><\/span><\/span> (corda) \u00e9 o <\/b><\/span><\/span><\/span>mesmo.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Reflex\u00e3o em meios bidimensionais<\/b><\/span><\/span><\/span><\/p>\n

A <\/b><\/span><\/span><\/span>reflex\u00e3o<\/b><\/span><\/span><\/span> de uma onda num <\/b><\/span><\/span><\/span>meio bidimensional, <\/b><\/span><\/span><\/span>como por exemplo, <\/b><\/span><\/span><\/span>na superf\u00edcie da \u00e1gua de uma cuba, <\/b><\/span><\/span><\/span>pode ocorrer em <\/b><\/span><\/span><\/span>duas situa\u00e7\u00f5es:<\/b><\/span><\/span><\/span><\/p>\n

\"\"\u00a0<\/span>Ondas circulares (esf\u00e9ricas)<\/b><\/span><\/span><\/span>\u00a0\"\"<\/b><\/span><\/span><\/span> <\/b>Quando a <\/b><\/span><\/span><\/span>ponta de uma r\u00e9gua <\/b><\/span><\/span><\/span>bate <\/b><\/span><\/span><\/span>continua<\/b><\/span><\/span><\/span> e <\/b><\/span><\/span><\/span>periodicamente na superf\u00edcie da \u00e1gua <\/b><\/span><\/span><\/span>origina <\/b><\/span><\/span><\/span>perturba\u00e7\u00f5es circulares (ondas circulares) <\/b><\/span><\/span><\/span>que se <\/b><\/span><\/span><\/span>movem na superf\u00edcie da \u00e1gua, afastando-se do ponto onde as perturba\u00e7\u00f5es s\u00e3o geradas.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Como determinar o formato das ondas circulares refletidas num obst\u00e1culo<\/b><\/span><\/span><\/span><\/p>\n

Considere as <\/b><\/span><\/span><\/span>ondas circulares (esf\u00e9ricas) <\/b><\/span><\/span><\/span>da figura 1, <\/b><\/span><\/span><\/span>produzidas pela fonte F<\/b><\/span><\/span><\/span> e que <\/b><\/span><\/span><\/span>incidem no obst\u00e1culo plano P.<\/b><\/span><\/span><\/span>\"\"<\/p>\n

F<\/b><\/span><\/span><\/span>A<\/b><\/span><\/span><\/sub><\/span> e <\/b><\/span><\/span><\/span>F<\/b><\/span><\/span><\/span>B<\/b><\/span><\/span><\/sub><\/span> s\u00e3o <\/b><\/span><\/span><\/span>dois raios de onda incidentes, <\/b><\/span><\/span><\/span>perpendiculares a <\/b><\/span><\/span><\/span>cada frente de onda <\/b><\/span><\/span><\/span>e que <\/b><\/span><\/span><\/span>indicam<\/b><\/span><\/span><\/span> a <\/b><\/span><\/span><\/span>dire\u00e7\u00e3o e sentido <\/b><\/span><\/span><\/span>de sua <\/b><\/span><\/span><\/span>propaga\u00e7\u00e3o.<\/b><\/span><\/span><\/span><\/p>\n

Ao <\/b><\/span><\/span><\/span>atingirem<\/b><\/span><\/span><\/span> o <\/b><\/span><\/span><\/span>obst\u00e1culo P <\/b><\/span><\/span><\/span>essas ondas <\/b><\/span><\/span><\/span>sofrem reflex\u00e3o <\/b><\/span><\/span><\/span>de modo que <\/b><\/span><\/span><\/span>cada ponto do obst\u00e1culo <\/b><\/span><\/span><\/span>torna-se <\/b><\/span><\/span><\/span>fonte de uma onda secund\u00e1ria. <\/b><\/span><\/span><\/span><\/p>\n

Pelo <\/b><\/span><\/span><\/span>princ\u00edpio da reflex\u00e3o <\/b><\/span><\/span><\/span>os <\/b><\/span><\/span><\/span>raios incidentes F<\/b><\/span><\/span><\/span>A<\/b><\/span><\/span><\/sub><\/span> e F<\/b><\/span><\/span><\/span>B<\/b><\/span><\/span><\/sub><\/span> <\/b>sofrem <\/b><\/span><\/span><\/span>reflex\u00e3o e retornam (AC e BD), <\/b><\/span><\/span><\/span>de modo que <\/b><\/span><\/span><\/span>os \u00e2ngulos i e r entre a normal N, e os raios incidente e refletido sejam iguais, ou seja, i = r (figura 2).<\/b><\/span><\/span><\/span><\/p>\n

Ent\u00e3o, <\/b><\/span><\/span><\/span>todos os raios refletidos se encontram em um ponto comum F\u2019<\/b><\/span><\/span><\/span>, e as <\/b><\/span><\/span><\/span>ondas refletidas se comportam como se fossem originadas por uma fonte F\u2019, sim\u00e9trica de F, em rela\u00e7\u00e3o ao obst\u00e1culo refletor P.<\/b><\/span><\/span><\/span>\"\"<\/p>\n

Assim, para voc\u00ea esquematizar as ondas refletidas, basta voc\u00ea localizar a fonte F\u2019, sim\u00e9trica a F e, a partir dela tra\u00e7ar as ondas refletidas, em vermelho na figura.<\/b><\/span><\/span><\/span><\/p>\n

Lembre-se de que\u00a0<\/b><\/span><\/span><\/span>a <\/b><\/span><\/span><\/span>velocidade de propaga\u00e7\u00e3o e o comprimento de onda <\/b><\/span><\/span><\/span>das <\/b><\/span><\/span><\/span>ondas incidentes <\/b><\/span><\/span><\/span>e <\/b><\/span><\/span><\/span>refletidas s\u00e3o os mesmos, pois o meio \u00e9 o mesmo.<\/b><\/span><\/span><\/span> <\/b><\/p>\n

A <\/b><\/span><\/span><\/span>frequ\u00eancia tamb\u00e9m n\u00e3o muda, \u00e9 a da fonte.<\/b><\/span><\/span><\/span><\/p>\n

\u00a0<\/span><\/p>\n

Ondas planas (retas)<\/b><\/span><\/span><\/span>\u00a0\"\" <\/b><\/span><\/span><\/span>Podem <\/b><\/span><\/span><\/span>ser produzidas <\/b><\/span><\/span><\/span>tocando-se <\/b><\/span><\/span><\/span>leve e continuamente <\/b><\/span><\/span><\/span>a <\/b><\/span><\/span><\/span>superf\u00edcie da \u00e1gua com uma r\u00e9gua (fonte) na posi\u00e7\u00e3o indicada na figura.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Como determinar o formato das ondas retas (planas) refletidas num obst\u00e1culo<\/b><\/span><\/span><\/span><\/p>\n

Considere as <\/b><\/span><\/span><\/span>ondas retas da figura 1<\/b><\/span><\/span><\/span>, <\/b><\/span><\/span><\/span>produzidas <\/b><\/span><\/span><\/span>pela <\/b><\/span><\/span><\/span>fonte F <\/b><\/span><\/span><\/span>e que <\/b><\/span><\/span><\/span>incidem <\/b><\/span><\/span><\/span>no <\/b><\/span><\/span><\/span>obst\u00e1culo plano P.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Pelo <\/b><\/span><\/span><\/span>princ\u00edpio da reflex\u00e3o <\/b><\/span><\/span><\/span>o <\/b><\/span><\/span><\/span>raio incidente F<\/b><\/span><\/span><\/span>A<\/b><\/span><\/span><\/sub><\/span> sofre reflex\u00e3o e retorna (AC), <\/b><\/span><\/span><\/span>de <\/b><\/span><\/span><\/span>modo<\/b><\/span><\/span><\/span> que os <\/b><\/span><\/span><\/span>\u00e2ngulos i e r entre a normal N, e o raio incidente e refletido sejam iguais, <\/b><\/span><\/span><\/span>ou seja, <\/b><\/span><\/span><\/span>i = r (figura 2) <\/b><\/span><\/span><\/span><\/p>\n

Lembre-se de que\u00a0<\/b><\/span><\/span><\/span>a <\/b><\/span><\/span><\/span>velocidade de propaga\u00e7\u00e3o e o comprimento de onda das ondas incidentes e<\/b><\/span><\/span><\/span> <\/b>refletidas s\u00e3o os mesmos, <\/b><\/span><\/span><\/span>pois o <\/b><\/span><\/span><\/span>meio \u00e9 o mesmo. <\/b><\/span><\/span><\/span><\/p>\n

A frequ\u00eancia tamb\u00e9m n\u00e3o muda, \u00e9 a da fonte.<\/b><\/span><\/span><\/span><\/p>\n

\u00a0<\/span><\/p>\n

O que voc\u00ea deve saber, informa\u00e7\u00f5es e dicas<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Conhecer o<\/b><\/span><\/span><\/span> comportamento da reflex\u00e3o de ondas em meios unidimensionais numa corda com extremidades fixas e livres.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Voc\u00ea deve saber como determinar <\/b><\/span><\/span><\/span>formato das ondas retas (planas) e circulares (esf\u00e9ricas) refletidas num obst\u00e1culo, <\/b><\/span><\/span><\/span>conforme explicado na teoria. <\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

N\u00e3o importa se o <\/b><\/span><\/span><\/span>meio \u00e9 uni, bi ou tridimensional, <\/b><\/span><\/span><\/span>na <\/b><\/span><\/span><\/span>reflex\u00e3o das ondas, as ondas incidentes<\/b><\/span><\/span><\/span> e <\/b><\/span><\/span><\/span>refletidas tem sempre a mesma velocidade de propaga\u00e7\u00e3o V <\/b><\/span><\/span><\/span>(o meio \u00e9 o mesmo), a <\/b><\/span><\/span><\/span>mesma freq\u00fc\u00eancia f <\/b><\/span><\/span><\/span>(a fonte \u00e9 a mesma) e <\/b><\/span><\/span><\/span>consequentemente o mesmo comprimento de onda\u03bb, <\/b><\/span><\/span><\/span>pois <\/b><\/span><\/span><\/span>V = \u03bb.f.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

A <\/b><\/span><\/span><\/span>amplitude A<\/b><\/span><\/span><\/span> da onda <\/b><\/span><\/span><\/span>n\u00e3o est\u00e1 relacionada com V, f e\u00a0\u03bb\u00a0<\/b><\/span><\/span><\/span>e <\/b><\/span><\/span><\/span>sim com a energia transportada <\/b><\/span><\/span><\/span>pela onda.<\/b><\/span><\/span><\/span><\/p>\n

Quanto maior a energia, maior a amplitude e vice-versa.<\/b><\/span><\/span><\/span><\/p>\n

\u00a0<\/span><\/p>\n

Exemplos de reflex\u00e3o de ondas planas:<\/b><\/span><\/span><\/span><\/p>\n

Nas figuras <\/b><\/span><\/span><\/span>I, II, III e IV, <\/b><\/span><\/span><\/span>est\u00e3o representas as <\/b><\/span><\/span><\/span>frentes de ondas retas (planas)<\/b><\/span><\/span><\/span> que <\/b><\/span><\/span><\/span>incidem<\/b><\/span><\/span><\/span> em <\/b><\/span><\/span><\/span>anteparos.<\/b><\/span><\/span><\/span> Os <\/b><\/span><\/span><\/span>sentidos <\/b><\/span><\/span><\/span>de <\/b><\/span><\/span><\/span>propaga\u00e7\u00e3o<\/b><\/span><\/span><\/span> est\u00e3o <\/b><\/span><\/span><\/span>representados<\/b><\/span><\/span><\/span> pelas <\/b><\/span><\/span><\/span>setas.<\/b><\/span><\/span><\/span><\/p>\n

Esboce,<\/b><\/span><\/span><\/span> em <\/b><\/span><\/span><\/span>cada caso,<\/b><\/span><\/span><\/span> as <\/b><\/span><\/span><\/span>frentes de onda ap\u00f3s a reflex\u00e3o.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

Lembre-se de que as <\/b><\/span><\/span><\/span>ondas refletidas tem sempre a mesma velocidade de propaga\u00e7\u00e3o, <\/b><\/span><\/span><\/span>a <\/b><\/span><\/span><\/span>mesma freq\u00fc\u00eancia (da fonte) <\/b><\/span><\/span><\/span>e o <\/b><\/span><\/span><\/span>mesmo comprimento de onda.<\/b><\/span><\/span><\/span><\/p>\n

\u00a0<\/span><\/p>\n

Refra\u00e7\u00e3o de ondas em meios unidimencionais<\/b><\/span><\/span><\/span><\/p>\n

Refra\u00e7\u00e3o de uma onda<\/b><\/span><\/span><\/span><\/p>\n

A <\/b><\/span><\/span><\/span>Refra\u00e7\u00e3o <\/b><\/span><\/span><\/span>de uma <\/b><\/span><\/span><\/span>onda <\/b><\/span><\/span><\/span>\u00e9 um <\/b><\/span><\/span><\/span>fen\u00f4meno que ocorre quando uma onda, muda seu meio inicial de propaga\u00e7\u00e3o <\/b><\/span><\/span><\/span>para outro meio <\/b><\/span><\/span><\/span>de caracter\u00edsticas diferentes, variando <\/b><\/span><\/span><\/span>sua <\/b><\/span><\/span><\/span>dire\u00e7\u00e3o de propaga\u00e7\u00e3o.<\/b><\/span><\/span><\/span><\/p>\n

Considere <\/b><\/span><\/span><\/span>duas cordas de diferentes densidades lineares de massa <\/b><\/span><\/span><\/span>(\u00b5 = m\/L), <\/b><\/span><\/span><\/span>unidas,<\/b><\/span><\/span><\/span> e o <\/b><\/span><\/span><\/span>sistema preso numa parede com uma das extremidades fixas.<\/b><\/span><\/span><\/span><\/p>\n

Vamos considerar tr\u00eas casos:<\/b><\/span><\/span><\/span><\/p>\n

\"\" 1<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sup><\/span> caso<\/b><\/span><\/span><\/span> \"\" <\/b><\/span><\/span><\/span>A <\/b><\/span><\/span><\/span>densidade linear (\u00b5) <\/b><\/span><\/span><\/span>das cordas \u00e9 a <\/b><\/span><\/span><\/span>mesma,<\/b><\/span><\/span><\/span> ou seja,\u00a0<\/b><\/span><\/span><\/span>\u00b5<\/b><\/span><\/span><\/span>1 <\/b><\/span><\/span><\/sub><\/span>= \u00b5<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span>.<\/b><\/span><\/span><\/span><\/p>\n

Quando <\/b><\/span><\/span><\/span>o pulso passa de uma corda para a outra, toda energia \u00e9 transmitida<\/b><\/span><\/span><\/span>, n\u00e3o ocorrer\u00e1 <\/b><\/span><\/span><\/span>reflex\u00e3o<\/b><\/span><\/span><\/span> e a <\/b><\/span><\/span><\/span>onda continua como se estivesse no mesmo meio, mantendo todas suas<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

caracter\u00edsticas (freq\u00fc\u00eancia, amplitude, velocidade e comprimento de onda).<\/b><\/span><\/span><\/span><\/p>\n

\"\" 2<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sup><\/span> caso<\/b><\/span><\/span><\/span> \"\"<\/b><\/span><\/span><\/span> A <\/b><\/span><\/span><\/span>densidade linear <\/b><\/span><\/span><\/span>da <\/b><\/span><\/span><\/span>primeira corda (\u00b5<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>)<\/b><\/span><\/span><\/span> \u00e9 <\/b><\/span><\/span><\/span>maior do que a da segunda (\u00b5<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span>)<\/b><\/span><\/span><\/span>, ou seja, <\/b><\/span><\/span><\/span>\u00b5<\/b><\/span><\/span><\/span>1 <\/b><\/span><\/span><\/sub><\/span>>\u00a0\u00b5<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span>.<\/b><\/span><\/span><\/span><\/p>\n

Quando o <\/b><\/span><\/span><\/span>pulso chega ao ponto de jun\u00e7\u00e3o das cordas, <\/b><\/span><\/span><\/span>ocorre ao <\/b><\/span><\/span><\/span>mesmo tempo refra\u00e7\u00e3o e reflex\u00e3o. Esse ponto (jun\u00e7\u00e3o) funciona <\/b><\/span><\/span><\/span>como uma <\/b><\/span><\/span><\/span>extremidade livre\u00a0 <\/b><\/span><\/span><\/span>e o <\/b><\/span><\/span><\/span>pulso refletido retorna sem invers\u00e3o de fase. <\/b><\/span><\/span><\/span><\/p>\n

O <\/b><\/span><\/span><\/span>pulso refratado <\/b><\/span><\/span><\/span>tem sempre a <\/b><\/span><\/span><\/span>mesma fase do incidente.<\/b><\/span><\/span><\/span><\/p>\n

Parte da energia do pulso incidente <\/b><\/span><\/span><\/span>\u00e9 <\/b><\/span><\/span><\/span>transmitida ao pulso refratado <\/b><\/span><\/span><\/span>e <\/b><\/span><\/span><\/span>parte ao pulso refletido<\/b><\/span><\/span><\/span>, <\/b><\/span><\/span><\/span>diminuindo<\/b><\/span><\/span><\/span> assim a <\/b><\/span><\/span><\/span>amplitude desses dois pulsos<\/b><\/span><\/span><\/span>, ou seja, <\/b><\/span><\/span><\/span>A > A<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>\u00a0e A > A<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span>.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

A <\/b><\/span><\/span><\/span>for\u00e7a de tra\u00e7\u00e3o (T) <\/b><\/span><\/span><\/span>nas <\/b><\/span><\/span><\/span>duas cordas \u00e9 a mesma <\/b><\/span><\/span><\/span>e a <\/b><\/span><\/span><\/span>velocidade em cada corda \u00e9 fornecida<\/b><\/span><\/span><\/span> por <\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Observe <\/b><\/span><\/span><\/span>na express\u00e3o acima <\/b><\/span><\/span><\/span>que a <\/b><\/span><\/span><\/span>velocidade V \u00e9 inversamente proporcional \u00e0 densidade linear\u00a0\u00b5, <\/b><\/span><\/span><\/span>assim, a <\/b><\/span><\/span><\/span>velocidade da onda na corda mais densa <\/b><\/span><\/span><\/span>\u201cmais pesada\u201d <\/b><\/span><\/span><\/span>\u00e9 menor do que a velocidade na corda menos densa <\/b><\/span><\/span><\/span>\u201cmais leve\u201d<\/b><\/span><\/span><\/span>. Ent\u00e3o, <\/b><\/span><\/span><\/span>V<\/b><\/span><\/span><\/span>2 <\/b><\/span><\/span><\/sub><\/span>> V<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>.<\/b><\/span><\/span><\/span><\/p>\n

A <\/b><\/span><\/span><\/span>freq\u00fc\u00eancia f<\/b><\/span><\/span><\/span> \u00e9 a <\/b><\/span><\/span><\/span>mesma nas duas cordas, <\/b><\/span><\/span><\/span>pois a<\/b><\/span><\/span><\/span> fonte \u00e9 a mesma.<\/b><\/span><\/span><\/span><\/p>\n

V = \u03bbf\u00a0 \"\"<\/b><\/span><\/span><\/span>\u00a0 <\/b><\/span><\/span><\/span>f = V\/\u03bb\u00a0 \"\"<\/b><\/span><\/span><\/span>\u00a0 f = V<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>\/\u03bb<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>\u00a0e f = V<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span>\/\u03bb<\/b><\/span><\/span><\/span>2 <\/b><\/span><\/span><\/sub><\/span> \"\"\u00a0\u00a0 <\/b><\/span><\/span><\/span>V<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>\/\u03bb<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>= V<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span>\/\u03bb<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span> (I)<\/b><\/span><\/span><\/span><\/p>\n

Observe na <\/b><\/span><\/span><\/span>express\u00e3o (I) <\/b><\/span><\/span><\/span>que, <\/b><\/span><\/span><\/span>quanto maior a velocidade V maior o comprimento de onda\u00a0\u03bb. <\/b><\/span><\/span><\/span>Portanto o <\/b><\/span><\/span><\/span>comprimento de onda da corda menos densa \u00e9 maior que o da corda mais densa.<\/b><\/span><\/span><\/span><\/p>\n

\u00a0<\/span><\/p>\n

\"\" 3<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sup><\/span> caso<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span> \"\" <\/b><\/span><\/span><\/span>A <\/b><\/span><\/span><\/span>densidade linear <\/b><\/span><\/span><\/span>da<\/b><\/span><\/span><\/span> primeira corda (\u00b5<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>) <\/b><\/span><\/span><\/span>\u00e9 <\/b><\/span><\/span><\/span>menor\u00a0do que a da segunda (\u00b5<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span>), <\/b><\/span><\/span><\/span>ou seja,<\/b><\/span><\/span><\/span>\u00a0\u00b5<\/b><\/span><\/span><\/span>1 <\/b><\/span><\/span><\/sub><\/span><\u00a0\u00b5<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span>.<\/b><\/span><\/span><\/span><\/p>\n

Quando o <\/b><\/span><\/span><\/span>pulso chega ao ponto de jun\u00e7\u00e3o das cordas<\/b><\/span><\/span><\/span>, ocorre ao <\/b><\/span><\/span><\/span>mesmo tempo refra\u00e7\u00e3o e reflex\u00e3o. Esse ponto <\/b><\/span><\/span><\/span>(jun\u00e7\u00e3o) funciona como uma <\/b><\/span><\/span><\/span>extremidade fixa <\/b><\/span><\/span><\/span>e o <\/b><\/span><\/span><\/span>pulso refletido retorna com invers\u00e3o de fase. <\/b><\/span><\/span><\/span><\/p>\n

O <\/b><\/span><\/span><\/span>pulso refratado tem sempre a mesma fase do incidente.<\/b><\/span><\/span><\/span><\/p>\n

Parte da energia do pulso incidente <\/b><\/span><\/span><\/span>\u00e9 transmitida ao <\/b><\/span><\/span><\/span>pulso refratado <\/b><\/span><\/span><\/span>e <\/b><\/span><\/span><\/span>parte ao pulso refletido, diminuindo assim a amplitude desses dois pulsos, <\/b><\/span><\/span><\/span>ou seja, <\/b><\/span><\/span><\/span>A > A<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>\u00a0e A > A<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span>.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

A <\/b><\/span><\/span><\/span>freq\u00fc\u00eancia (f) desses dois pulsos<\/b><\/span><\/span><\/span> \u00e9 a <\/b><\/span><\/span><\/span>mesma, pois a fonte <\/b><\/span><\/span><\/span>\u00e9<\/b><\/span><\/span><\/span> a mesma. V<\/b><\/span><\/span><\/span>1 <\/b><\/span><\/span><\/sub><\/span>> V<\/b><\/span><\/span><\/span>2 \u00a0<\/b><\/span><\/span><\/sub><\/span>e\u00a0\u03bb<\/b><\/span><\/span><\/span>1 <\/b><\/span><\/span><\/sub><\/span>> \u03bb<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span>.<\/b><\/span><\/span><\/span><\/p>\n

\u00a0<\/span><\/p>\n

Refra\u00e7\u00e3o de ondas em meios bidimensionais<\/b><\/span><\/span><\/span><\/p>\n

Na <\/b><\/span><\/span><\/span>refra\u00e7\u00e3o a<\/b><\/span><\/span><\/span>\u00a0freq\u00fc\u00eancia<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>das <\/b><\/span><\/span><\/span>ondas incidentes\u00a0<\/b><\/span><\/span><\/span>\u00e9 a mesma\u00a0<\/b><\/span><\/span><\/span>que das ondas refratadas <\/b><\/span><\/span><\/span>(a fonte \u00e9 a mesma) e, como <\/b><\/span><\/span><\/span>V = \u03bbf\u00a0 \"\"<\/b><\/span><\/span><\/span>\u00a0 f = V\/\u03bb\u00a0 \"\"\u00a0<\/b><\/span><\/span><\/span>V e\u00a0\u03bb\u00a0s\u00e3o diretamente proporcionais <\/b><\/span><\/span><\/span>(maior V, maior \u03bb\u00a0e vice versa).<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Considere <\/b><\/span><\/span><\/span>dois meios diferentes 1 e 2 <\/b><\/span><\/span><\/span>e <\/b><\/span><\/span><\/span>ondas retas (planas) <\/b><\/span><\/span><\/span>se propagando <\/b><\/span><\/span><\/span>no meio 1, <\/b><\/span><\/span><\/span>com <\/b><\/span><\/span><\/span>velocidade V<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>\u00a0e comprimento de onda\u00a0\u03bb<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>,<\/b><\/span><\/span><\/span> que v\u00e3o incidir no<\/b><\/span><\/span><\/span> meio 2, com velocidade V<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span> e comprimento de onda \u03bb<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span> e, com V<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span> > V<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span>. <\/b><\/span><\/span><\/span>(figura I).<\/b><\/span><\/span><\/span><\/p>\n

\u00a0<\/span><\/p>\n

Sendo a <\/b><\/span><\/span><\/span>velocidade da onda do meio 1 maior<\/b><\/span><\/span><\/span> que a <\/b><\/span><\/span><\/span>velocidade da onda no meio 2, <\/b><\/span><\/span><\/span>o <\/b><\/span><\/span><\/span>raio de onda, <\/b><\/span><\/span><\/span>ao penetrar no <\/b><\/span><\/span><\/span>meio 2 se aproximar\u00e1 da normal, com i > r e com \u03bb<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span> > \u03bb<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span>.<\/b><\/span><\/span><\/span><\/p>\n

As <\/b><\/span><\/span><\/span>figuras II e III<\/b><\/span><\/span><\/span> mostram as <\/b><\/span><\/span><\/span>etapas da refra\u00e7\u00e3o.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Informa\u00e7\u00f5es e f\u00f3rmulas necess\u00e1rias para a resolu\u00e7\u00e3o de exerc\u00edcios sobre refra\u00e7\u00e3o de ondas planas<\/b><\/span><\/span><\/span><\/p>\n

Na\u00a0 <\/b><\/span><\/span><\/span>figura abaixo, AB <\/b><\/span><\/span><\/span>representa o <\/b><\/span><\/span><\/span>raio de onda incidente, CD o raio de onda refratado, i<\/b><\/span><\/span><\/span> o <\/b><\/span><\/span><\/span>\u00e2ngulo de incid\u00eancia <\/b><\/span><\/span><\/span>e <\/b><\/span><\/span><\/span>r<\/b><\/span><\/span><\/span> o <\/b><\/span><\/span><\/span>\u00e2ngulo de refra\u00e7\u00e3o, <\/b><\/span><\/span><\/span>bem como as <\/b><\/span><\/span><\/span>rela\u00e7\u00f5es matem\u00e1ticas entre os elementos que envolvem o fen\u00f4meno da <\/b><\/span><\/span><\/span>refra\u00e7\u00e3o de ondas planas.<\/b><\/span><\/span><\/span><\/p>\n

\"\"\"\"<\/p>\n

Na <\/b><\/span><\/span><\/span>refra\u00e7\u00e3o a<\/b><\/span><\/span><\/span>\u00a0freq\u00fc\u00eancia<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>das <\/b><\/span><\/span><\/span>ondas incidentes\u00a0<\/b><\/span><\/span><\/span>\u00e9 a mesma\u00a0<\/b><\/span><\/span><\/span>que das ondas refratadas <\/b><\/span><\/span><\/span>(a fonte \u00e9 a mesma) e, como <\/b><\/span><\/span><\/span>V = \u03bbf\u00a0 \"\"<\/b><\/span><\/span><\/span>\u00a0 f = V\/\u03bb\u00a0 \"\"\u00a0<\/b><\/span><\/span><\/span>V e\u00a0\u03bb\u00a0s\u00e3o diretamente proporcionais <\/b><\/span><\/span><\/span>(maior V, maior \u03bb\u00a0e vice versa).<\/b><\/span><\/span><\/span><\/p>\n

Baseado nas express\u00f5es acima voc\u00ea pode concluir que:<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Observa\u00e7\u00e3o:<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Dentro de certos limites as <\/b><\/span><\/span><\/span>express\u00f5es acima tamb\u00e9m s\u00e3o v\u00e1lidas para refraa\u00e7\u00e3o de ondas circulares (esf\u00e9ricas)\u00a0<\/b><\/span><\/span><\/span><\/p>\n

 <\/p>\n

O que voc\u00ea deve saber, informa\u00e7\u00f5es e dicas<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Conhecer o<\/b><\/span><\/span><\/span> comportamento da refra\u00e7\u00e3o de ondas <\/b><\/span><\/span><\/span>em meios <\/b><\/span><\/span><\/span>unidimensionais numa corda, <\/b><\/span><\/span><\/span>nos<\/b><\/span><\/span><\/span> tr\u00eas casos, <\/b><\/span><\/span><\/span>quando passa se deslocar em <\/b><\/span><\/span><\/span>meios de diferentes densidades lineares de massa. <\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Voc\u00ea deve saber como determinar <\/b><\/span><\/span><\/span>formato das ondas retas (planas) e circulares (esf\u00e9ricas), refratadas numa determinada superf\u00edcie de separa\u00e7\u00e3o, <\/b><\/span><\/span><\/span>conforme explicado na teoria. <\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Informa\u00e7\u00f5es e f\u00f3rmulas necess\u00e1rias para a resolu\u00e7\u00e3o de exerc\u00edcios sobre refra\u00e7\u00e3o de ondas planas<\/b><\/span><\/span><\/span><\/p>\n

\"\"\"\"<\/p>\n

Na <\/b><\/span><\/span><\/span>refra\u00e7\u00e3o a<\/b><\/span><\/span><\/span>\u00a0freq\u00fc\u00eancia<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>das <\/b><\/span><\/span><\/span>ondas incidentes\u00a0<\/b><\/span><\/span><\/span>\u00e9 a mesma\u00a0<\/b><\/span><\/span><\/span>que das ondas refratadas <\/b><\/span><\/span><\/span>(a fonte \u00e9 a mesma) e, como <\/b><\/span><\/span><\/span>V = \u03bbf\u00a0 \"\"<\/b><\/span><\/span><\/span>\u00a0 f = V\/\u03bb\u00a0 \"\"\u00a0<\/b><\/span><\/span><\/span>V e\u00a0\u03bb\u00a0s\u00e3o diretamente proporcionais <\/b><\/span><\/span><\/span>(maior V, maior \u03bb\u00a0e vice versa).<\/b><\/span><\/span><\/span><\/p>\n

Baseado na <\/b><\/span><\/span><\/span>lei de Snell-Descartes<\/b><\/span><\/span><\/span> <\/b>n<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>.seni = n<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span>.senr = constante <\/b><\/span><\/span><\/span>para o <\/b><\/span><\/span><\/span>mesmo <\/b><\/span><\/span><\/span>sistema de meios, voc\u00ea conclui que <\/b><\/span><\/span><\/span>n.sen\u03b1 = constante <\/b><\/span><\/span><\/span>e que o <\/b><\/span><\/span><\/span>\u00edndice de refra\u00e7\u00e3o n de um meio \u00e9 inversamente proporcional ao seno do \u00e2ngulo que o raio forma com esse meio.<\/b><\/span><\/span><\/span><\/p>\n

Consequentemente <\/b><\/span><\/span><\/span>n \u00e9 inversamente proporcional a \u03b1<\/b><\/span><\/span><\/span>, portanto <\/b><\/span><\/span><\/span>maior n, menor \u03b1.<\/b><\/span><\/span><\/span><\/p>\n

Baseado nas express\u00f5es acima voc\u00ea pode concluir que:<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Observa\u00e7\u00e3o:<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Dentro de certos limites as <\/b><\/span><\/span><\/span>express\u00f5es acima tamb\u00e9m s\u00e3o v\u00e1lidas para refra\u00e7\u00e3o de ondas circulares (esf\u00e9ricas)\u00a0<\/b><\/span><\/span><\/span><\/p>\n

 <\/p>\n

\"\"<\/p>\n

Para <\/b><\/span><\/span><\/span>esbo\u00e7ar<\/b><\/span><\/span><\/span> as <\/b><\/span><\/span><\/span>ondas planas refratadas num dado exerc\u00edcio, <\/b><\/span><\/span><\/span>voc\u00ea deve <\/b><\/span><\/span><\/span>seguir as etapas, apresentas no exemplo a seguir:<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Na<\/b><\/span><\/span><\/span> figura ao lado, <\/b><\/span><\/span><\/span>esquematizar as <\/b><\/span><\/span><\/span>ondas planas refratadas no meio B, <\/b><\/span><\/span><\/span>a partir das <\/b><\/span><\/span><\/span>ondas esquematizadas no meio A. <\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

1<\/b><\/span><\/span><\/span>a<\/b><\/span><\/span><\/sup><\/span> etapa<\/b><\/span><\/span><\/span> \u00a0\"\"<\/b><\/span><\/span><\/span> <\/b>Tra\u00e7ar<\/b><\/span><\/span><\/span> o <\/b><\/span><\/span><\/span>raio de onda incidente <\/b><\/span><\/span><\/span>(r<\/b><\/span><\/span><\/span>i<\/b><\/span><\/span><\/sub><\/span>) que \u00e9 sempre <\/b><\/span><\/span><\/span>perpendicular \u00e0s frentes de onda.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

2<\/b><\/span><\/span><\/span>a<\/b><\/span><\/span><\/sup><\/span> etapa<\/b><\/span><\/span><\/span>\u00a0\"\"<\/b><\/span><\/span><\/span> <\/b>Tra\u00e7ar<\/b><\/span><\/span><\/span> o <\/b><\/span><\/span><\/span>raio de onda refratado (r<\/b><\/span><\/span><\/span>r<\/b><\/span><\/span><\/sub><\/span>), <\/b><\/span><\/span><\/span>o <\/b><\/span><\/span><\/span>\u00e2ngulo de incid\u00eancia (i), <\/b><\/span><\/span><\/span>a <\/b><\/span><\/span><\/span>normal (N) <\/b><\/span><\/span><\/span>e o <\/b><\/span><\/span><\/span>\u00e2ngulo de refra\u00e7\u00e3o (r).<\/b><\/span><\/span><\/span> <\/b>Supondo n<\/b><\/span><\/span><\/span>A <\/b><\/span><\/span><\/sub><\/span>< n<\/b><\/span><\/span><\/span>B<\/b><\/span><\/span><\/sub><\/span>, teremos <\/b><\/span><\/span><\/span>que\u00a0<\/b><\/span><\/span><\/span>\u03bb<\/b><\/span><\/span><\/span>A <\/b><\/span><\/span><\/sub><\/span>> \u03bb<\/b><\/span><\/span><\/span>B<\/b><\/span><\/span><\/sub><\/span>, V<\/b><\/span><\/span><\/span>A <\/b><\/span><\/span><\/sub><\/span>> V<\/b><\/span><\/span><\/span>B\u00a0 <\/b><\/span><\/span><\/sub><\/span>e r < i <\/b><\/span><\/span><\/span>(veja informa\u00e7\u00f5es na teoria).<\/b><\/span><\/span><\/span><\/p>\n

3<\/b><\/span><\/span><\/span>a<\/b><\/span><\/span><\/sup><\/span> etapa\u00a0\"\"<\/b><\/span><\/span><\/span> Utilizar a <\/b><\/span><\/span><\/span>equa\u00e7\u00e3o fundamental da ondulat\u00f3ria\u00a0<\/b><\/span><\/span><\/span>V = \u03bb.f.<\/b><\/span><\/span><\/span><\/p>\n

\u00a0<\/span><\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

Se <\/b><\/span><\/span><\/span>houver refra\u00e7\u00e3o, sempre<\/b><\/span><\/span><\/span> ocorrer\u00e1 tamb\u00e9m <\/b><\/span><\/span><\/span>reflex\u00e3o.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

As express\u00f5es:<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

s\u00e3o <\/b><\/span><\/span><\/span>v\u00e1lidas<\/b><\/span><\/span><\/span> tamb\u00e9m para <\/b><\/span><\/span><\/span>ondas eletromagn\u00e9ticas, <\/b><\/span><\/span><\/span>como por exemplo, a <\/b><\/span><\/span><\/span>luz.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

\u00a0<\/span><\/p>\n

\"\"<\/p>\n

A <\/b><\/span><\/span><\/span>freq\u00fc\u00eancia <\/b><\/span><\/span><\/span>\u00e9 <\/b><\/span><\/span><\/span>caracter\u00edstica da fonte <\/b><\/span><\/span><\/span>e <\/b><\/span><\/span><\/span>independe do meio. <\/b><\/span><\/span><\/span>Assim, por exemplo, <\/b><\/span><\/span><\/span>se uma fonte luminosa emitir um feixe de luz azul (freq\u00fc\u00eancia 7.10<\/b><\/span><\/span><\/span>14<\/b><\/span><\/span><\/sup><\/span>\u00a0Hz), <\/b><\/span><\/span><\/span>em qualquer meio que este <\/b><\/span><\/span><\/span>feixe luminoso estiver se propagando ele sempre ser\u00e1 azul, pois ter\u00e1 sempre essa frequ\u00eancia.<\/b><\/span><\/span><\/span><\/p>\n

O mesmo \u00e9 v\u00e1lido para ondas.\u00a0<\/b><\/span><\/span><\/span><\/p>\n

\u00a0<\/span><\/p>\n

\"\"<\/p>\n

Alguns exerc\u00edcios interessantes resolvidos para que voc\u00ea possa se aprofundar no assunto:<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Resolu\u00e7\u00e3o:<\/b><\/span><\/span><\/span><\/p>\n

a) V = \u03bb.f\u00a0 \"\"<\/b><\/span><\/span><\/span>\u00a0 V = 6.50\u00a0 \"\"\u00a0\u00a0<\/b><\/span><\/span><\/span>V = 300m\/s.<\/b><\/span><\/span><\/span><\/p>\n

b) intervalo de tempo (\u0394t<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>) <\/b><\/span><\/span><\/span>que a <\/b><\/span><\/span><\/span>onda demora\u00a0 <\/b><\/span><\/span><\/span>para ir de <\/b><\/span><\/span><\/span>A at\u00e9 B\u00a0 \"\"<\/b><\/span><\/span><\/span>\u00a0 <\/b><\/span><\/span><\/span>V = \u0394S\/\u0394t<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>\u00a0 \"\"\u00a0 300 = 30\/\u0394t<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span><\/p>\n

\"\" \u0394t<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>\u00a0=1\/10s<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

c)<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

02-(PUCC-SP)<\/b><\/span><\/span><\/span> <\/b>Na <\/b><\/span><\/span><\/span>superf\u00edcie<\/b><\/span><\/span><\/span> da <\/b><\/span><\/span><\/span>\u00e1gua<\/b><\/span><\/span><\/span> parada de um <\/b><\/span><\/span><\/span>tanque quadrado de 30cm de lado, <\/b><\/span><\/span><\/span>provoca-se <\/b><\/span><\/span><\/span><\/p>\n

no <\/b><\/span><\/span><\/span>centro do mesmo <\/b><\/span><\/span><\/span>uma <\/b><\/span><\/span><\/span>onda que se propaga com frentes de onda circulares, <\/b><\/span><\/span><\/span>com <\/b><\/span><\/span><\/span>freq\u00fc\u00eancia de 5Hz e velocidade de 8cm\/s.<\/b><\/span><\/span><\/span> <\/b>\"\"<\/p>\n

a) Represente<\/b><\/span><\/span><\/span> a <\/b><\/span><\/span><\/span>configura\u00e7\u00e3o<\/b><\/span><\/span><\/span> da <\/b><\/span><\/span><\/span>frente de onda, depois de 2s de sua gera\u00e7\u00e3o.<\/b><\/span><\/span><\/span><\/p>\n

b) <\/b><\/span><\/span><\/span>As <\/b><\/span><\/span><\/span>ondas, ao se refletirem na parede do tanque retornam com, ou sem invers\u00e3o de fase? <\/b><\/span><\/span><\/span><\/p>\n

Justifique<\/b><\/span><\/span><\/span><\/p>\n

Resolu\u00e7\u00e3o:<\/b><\/span><\/span><\/span><\/p>\n

a) C\u00e1lculo<\/b><\/span><\/span><\/span> da <\/b><\/span><\/span><\/span>dist\u00e2ncia percorrida <\/b><\/span><\/span><\/span>pela onda <\/b><\/span><\/span><\/span>em 2s\u00a0 \"\"<\/b><\/span><\/span><\/span>\u00a0 <\/b><\/span><\/span><\/span>V = \u0394S\/\u0394t\u00a0 \"\"<\/b><\/span><\/span><\/span> \u00a0 8 = \u0394S\/2\u00a0 \"\" \u00a0<\/b><\/span><\/span><\/span>\u0394S = 16cm.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Aplicando o <\/b><\/span><\/span><\/span>teorema de Pit\u00e1goras <\/b><\/span><\/span><\/span>no <\/b><\/span><\/span><\/span>tri\u00e2ngulo OCD \"\"<\/b><\/span><\/span><\/span> <\/b>d<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span> = 15<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span> + 15<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span> <\/b>= 2.15<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span> \"\"<\/b><\/span><\/span><\/span> <\/b>d = 15\"\" <\/b><\/span><\/span><\/span>= 15.1,4<\/b><\/span><\/span><\/span><\/p>\n

\"\" d = 21 cm.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Observe nas <\/b><\/span><\/span><\/span>figuras acima e na figura ao lado <\/b><\/span><\/span><\/span>que, em <\/b><\/span><\/span><\/span>t = 2s,<\/b><\/span><\/span><\/span> a onda <\/b><\/span><\/span><\/span>n\u00e3o chegou aos pontos A,C,E e G <\/b><\/span><\/span><\/span>e que <\/b><\/span><\/span><\/span>j\u00e1 est\u00e1 voltando dos pontos B, D, F e H.<\/b><\/span><\/span><\/span><\/p>\n

b) Sem invers\u00e3o de fase, <\/b><\/span><\/span><\/span>pois as <\/b><\/span><\/span><\/span>paredes comportam-se<\/b><\/span><\/span><\/span> como <\/b><\/span><\/span><\/span>extremidades livres.<\/b><\/span><\/span><\/span><\/p>\n

03-(FUVEST-SP)<\/b><\/span><\/span><\/span> <\/b>Um <\/b><\/span><\/span><\/span>canal de navega\u00e7\u00e3o de 4,0m de largura <\/b><\/span><\/span><\/span>tem suas <\/b><\/span><\/span><\/span>comportas semi-abertas, <\/b><\/span><\/span><\/span>como est\u00e1 indicado na figura. <\/b><\/span><\/span><\/span>Ondas planas propagam-se na superf\u00edcie da \u00e1gua do canal <\/b><\/span><\/span><\/span>com <\/b><\/span><\/span><\/span>velocidade igual a 2,0m\/s.<\/b><\/span><\/span><\/span> Considere uma <\/b><\/span><\/span><\/span>crista AB,<\/b><\/span><\/span><\/span> na <\/b><\/span><\/span><\/span>posi\u00e7\u00e3o indicada <\/b><\/span><\/span><\/span>na figura, no <\/b><\/span><\/span><\/span>instante t=0.<\/b><\/span><\/span><\/span>\"\"<\/p>\n

Esboce a <\/b><\/span><\/span><\/span>configura\u00e7\u00e3o dessa crista <\/b><\/span><\/span><\/span>depois de <\/b><\/span><\/span><\/span>decorridos 1,5s,<\/b><\/span><\/span><\/span> <\/b>indicando a dist\u00e2ncia, em metros, entre seus extremos A\u2019B\u2019 nessa configura\u00e7\u00e3o <\/b><\/span><\/span><\/span>(despreze efeitos da difra\u00e7\u00e3o).<\/b><\/span><\/span><\/span><\/p>\n

Resolu\u00e7\u00e3o:<\/b><\/span><\/span><\/span><\/p>\n

Vamos <\/b><\/span><\/span><\/span>calcular<\/b><\/span><\/span><\/span> a <\/b><\/span><\/span><\/span>dist\u00e2ncia percorrida <\/b><\/span><\/span><\/span>por <\/b><\/span><\/span><\/span>cada ponto da onda<\/b><\/span><\/span><\/span> no <\/b><\/span><\/span><\/span>instante t = 1,5 s\u00a0 \"\"<\/b><\/span><\/span><\/span>\u00a0 <\/b><\/span><\/span><\/span>V = \u0394S\/\u0394t<\/b><\/span><\/span><\/span><\/p>\n

\"\" \u00a02 = \u0394S\/1,5\u00a0 \"\"\u00a0\u00a0<\/b><\/span><\/span><\/span>\u0394S = 3,0m.<\/b><\/span><\/span><\/span><\/p>\n

Verifique <\/b><\/span><\/span><\/span>nas figuras abaixo <\/b><\/span><\/span><\/span>que\u00a0 \"\"\u00a0 <\/b><\/span><\/span><\/span>AA\u2019 = BB\u2019 = \u0394S = 3,0m <\/b><\/span><\/span><\/span>e que <\/b><\/span><\/span><\/span>PP\u2019 = QO\u2019 = \u0394S = 3,0m.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Quando t = 1,5s:<\/b><\/span><\/span><\/span><\/p>\n

Os pontos da onda entre A\u2019 e P\u2019<\/b><\/span><\/span><\/span> j\u00e1 atingiram o anteparo e <\/b><\/span><\/span><\/span>est\u00e3o retornando. <\/b><\/span><\/span><\/span>O <\/b><\/span><\/span><\/span>mesmo acontece <\/b><\/span><\/span><\/span>com os <\/b><\/span><\/span><\/span>pontos da onda entre B\u2019 e Q\u2019.<\/b><\/span><\/span><\/span><\/p>\n

Os <\/b><\/span><\/span><\/span>pontos P\u2019 e Q\u2019 est\u00e3o no anteparo.<\/b><\/span><\/span><\/span><\/p>\n

Os <\/b><\/span><\/span><\/span>pontos da onda entre P\u2019 e Q\u2019 <\/b><\/span><\/span><\/span>ainda n\u00e3o <\/b><\/span><\/span><\/span>atingiram o anteparo <\/b><\/span><\/span><\/span>e est\u00e3o <\/b><\/span><\/span><\/span>se deslocando para a direita.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Se voc\u00ea deseja <\/b><\/span><\/span><\/span>ainda mais se aprofundar no assunto <\/b><\/span><\/span><\/span>confira as <\/b><\/span><\/span><\/span>resolu\u00e7\u00f5es dos exerc\u00edcios de n\u00fameros 03, 04, 06, 11, 17, 24, 32, 38 e 43.<\/b><\/span><\/span><\/span><\/p>\n

 <\/p>\n

Confira os exerc\u00edcios!<\/span><\/a><\/h3>\n","protected":false},"excerpt":{"rendered":"

Reflex\u00e3o e Refra\u00e7\u00e3o de Ondas Reflex\u00e3o de uma onda Uma onda sofre reflex\u00e3o quando, propagando-se em um dado meio, atinge a interface de separa\u00e7\u00e3o com outro meio e, em seguida, volta a se propagar no meio inicial. Reflex\u00e3o em meios unidimensionais A reflex\u00e3o de uma onda num meio unidimensional, como por exemplo, numa corda, pode ocorrer em duas situa\u00e7\u00f5es: Extremidade<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":2398,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"om_disable_all_campaigns":false,"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"class_list":["post-2410","page","type-page","status-publish","hentry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/2410","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/comments?post=2410"}],"version-history":[{"count":2,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/2410\/revisions"}],"predecessor-version":[{"id":2418,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/2410\/revisions\/2418"}],"up":[{"embeddable":true,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/2398"}],"wp:attachment":[{"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/media?parent=2410"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}