{"id":2428,"date":"2016-09-11T00:36:00","date_gmt":"2016-09-11T00:36:00","guid":{"rendered":"http:\/\/fisicaevestibular.com.br\/novo\/?page_id=2428"},"modified":"2024-08-23T15:04:50","modified_gmt":"2024-08-23T15:04:50","slug":"equacao-da-onda-equacao-fundamental-da-ondulatoria","status":"publish","type":"page","link":"https:\/\/fisicaevestibular.com.br\/novo\/ondulatoria\/ondas\/equacao-da-onda-equacao-fundamental-da-ondulatoria\/","title":{"rendered":"Equa\u00e7\u00e3o da onda (Equa\u00e7\u00e3o fundamental da ondulat\u00f3ria)"},"content":{"rendered":"

Equa\u00e7\u00e3o da onda (Equa\u00e7\u00e3o fundamental da ondulat\u00f3ria)<\/b><\/span><\/span><\/span><\/p>\n

Elementos de uma onda<\/b><\/span><\/span><\/span><\/p>\n

Considere a <\/b><\/span><\/span><\/span>onda peri\u00f3dica (sucess\u00e3o de pulsos iguais em tempos iguais) <\/b><\/span><\/span><\/span>das figurasa seguir, cujas <\/b><\/span><\/span><\/span>principais caracter\u00edsticas s\u00e3o:<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

\"\"\u00a0 <\/span>Comprimento de onda (\u03bb<\/b><\/span><\/span><\/span>)<\/b><\/span><\/span><\/span>\u00a0\"\"<\/b><\/span><\/span><\/span> representa a dist\u00e2ncia percorrida pela onda at\u00e9 come\u00e7ar <\/b><\/span><\/span><\/span>novamente a repeti\u00e7\u00e3o, <\/b><\/span><\/span><\/span>ou seja, \u00e9 a <\/b><\/span><\/span><\/span>menor dist\u00e2ncia entre dois pontos consecutivos <\/b><\/span><\/span><\/span>que est\u00e3o em <\/b><\/span><\/span><\/span>concor-d\u00e2ncia de fase, <\/b><\/span><\/span><\/span>como por exemplo, a <\/b><\/span><\/span><\/span>menor dist\u00e2ncia entre duas cristas ou dois vales.<\/b><\/span><\/span><\/span>\"\"<\/p>\n

\"\" Per\u00edodo (T)<\/b><\/span><\/span><\/span>\u00a0\"\"<\/b><\/span><\/span><\/span> <\/b>tempo<\/b><\/span><\/span><\/span> que a <\/b><\/span><\/span><\/span>onda demora\u00a0<\/b><\/span><\/span><\/span>para <\/b><\/span><\/span><\/span>percorrer um comprimento de onda <\/b><\/span><\/span><\/span>(1\u03bb),<\/b><\/span><\/span><\/span> <\/b>que \u00e9 o <\/b><\/span><\/span><\/span>mesmo tempo que um ponto qualquer da onda demora <\/b><\/span><\/span><\/span>para <\/b><\/span><\/span><\/span>efetuar uma oscila\u00e7\u00e3o <\/b><\/span><\/span><\/span>(vai e vem) <\/b><\/span><\/span><\/span>completa<\/b><\/span><\/span><\/span> e que <\/b><\/span><\/span><\/span>\u00e9 o mesmo tempo que a fonte demora para gerar uma onda completa.<\/b><\/span><\/span><\/span>\"\"<\/p>\n

Na <\/b><\/span><\/span><\/span>figura acima, <\/b><\/span><\/span><\/span>o <\/b><\/span><\/span><\/span>per\u00edodo <\/b><\/span><\/span><\/span>T<\/b><\/span><\/span><\/span> \u00e9 o <\/b><\/span><\/span><\/span>tempo compreendido entre os instantes T = t<\/b><\/span><\/span><\/span>4 <\/b><\/span><\/span><\/sub><\/span>– t<\/b><\/span><\/span><\/span>o <\/b><\/span><\/span><\/sub><\/span>= t<\/b><\/span><\/span><\/span>5 <\/b><\/span><\/span><\/sub><\/span>– t<\/b><\/span><\/span><\/span>1 <\/b><\/span><\/span><\/sub><\/span>= t<\/b><\/span><\/span><\/span>6 <\/b><\/span><\/span><\/sub><\/span>– t<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span>, etc.<\/b><\/span><\/span><\/span><\/p>\n

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

\"\" Frequ\u00eancia (f)<\/b><\/span><\/span><\/span>\u00a0\"\"<\/b><\/span><\/span><\/span> A <\/b><\/span><\/span><\/span>frequ\u00eancia (f) <\/b><\/span><\/span><\/span>representa <\/b><\/span><\/span><\/span>quantas oscila\u00e7\u00f5es completas uma onda efetua<\/b><\/span><\/span><\/span><\/p>\n

em <\/b><\/span><\/span><\/span>cada unidade de tempo, <\/b><\/span><\/span><\/span>ou ainda, <\/b><\/span><\/span><\/span>quantos comprimentos de onda passam por um ponto da onda em cada unidade de tempo.<\/b><\/span><\/span><\/span>\"\"<\/p>\n

Se o <\/b><\/span><\/span><\/span>per\u00edodo T estiver em segundos (s) a freq\u00fc\u00eancia estar\u00e1 em hertz (Hz), <\/b><\/span><\/span><\/span>que significa <\/b><\/span><\/span><\/span>ciclos por segundo. <\/b><\/span><\/span><\/span><\/p>\n

Exemplo:<\/b><\/span><\/span><\/span> Se a <\/b><\/span><\/span><\/span>frequ\u00eancia<\/b><\/span><\/span><\/span> de uma onda <\/b><\/span><\/span><\/span>for de 60 Hz<\/b><\/span><\/span><\/span>, isto significa que a <\/b><\/span><\/span><\/span>fonte ou qualquer ponto desta onda oscila 60 vezes em cada segundo.<\/b><\/span><\/span><\/span><\/p>\n

Rela\u00e7\u00e3o importante<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Velocidade V de propaga\u00e7\u00e3o da onda (Equa\u00e7\u00e3o fundamental da ondulat\u00f3ria)<\/b><\/span><\/span><\/span><\/p>\n

Supondo o <\/b><\/span><\/span><\/span>meio homog\u00eaneo, <\/b><\/span><\/span><\/span>a <\/b><\/span><\/span><\/span>onda <\/b><\/span><\/span><\/span>se <\/b><\/span><\/span><\/span>propaga nele com velocidade constante<\/b><\/span><\/span><\/span>, dada por<\/b><\/span><\/span><\/span><\/p>\n

V =\u00a0\"\"S\/\"\"t.<\/b><\/span><\/span><\/span><\/p>\n

Mas, observe que, <\/b><\/span><\/span><\/span>quando\u00a0\"\"S = 1\u03bb,\u00a0\"\"t = T<\/b><\/span><\/span><\/span>, pois o <\/b><\/span><\/span><\/span>per\u00edodo T \u00e9 o tempo que a onda demora para percorrer um comprimento de onda (1\u03bb).<\/b><\/span><\/span><\/span><\/p>\n

V =\u00a0\"\"S\/\"\"t<\/b><\/span><\/span><\/span> \u00a0\"\"\u00a0 <\/b><\/span><\/span><\/span>V =\u00a0<\/b><\/span><\/span><\/span>\u03bb<\/b><\/span><\/span><\/span><\/span>\/T\u00a0 \"\"<\/b><\/span><\/span><\/span> \u00a0V =\u00a0<\/b><\/span><\/span><\/span>\u03bb<\/b><\/span><\/span><\/span><\/span>\/(1\/f)\u00a0 \"\"\u00a0\u00a0<\/b><\/span><\/span><\/span>V =\u00a0<\/b><\/span><\/span><\/span>\u03bb<\/b><\/span><\/span><\/span><\/span>.f (essa equa\u00e7\u00e3o \u00e9 chamada equa\u00e7\u00e3o fundamental da ondulat\u00f3ria).<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Velocidade de propaga\u00e7\u00e3o dos pulsos nos meios unidimensionais (corda)<\/b><\/span><\/span><\/span><\/p>\n

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

Considere um <\/b><\/span><\/span><\/span>pulso ou v\u00e1rios pulsos sucessivos (onda) <\/b><\/span><\/span><\/span>se <\/b><\/span><\/span><\/span>propagando<\/b><\/span><\/span><\/span> com <\/b><\/span><\/span><\/span>velocidade V <\/b><\/span><\/span><\/span>numa<\/b><\/span><\/span><\/span><\/p>\n

corda tracionada <\/b><\/span><\/span><\/span>(esticada) por uma <\/b><\/span><\/span><\/span>for\u00e7a de intensidade F.<\/b><\/span><\/span><\/span><\/p>\n

Denominamos<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>densidade linear de massa (\u00b5)<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>de uma <\/b><\/span><\/span><\/span>corda homog\u00eanea, <\/b><\/span><\/span><\/span>de <\/b><\/span><\/span><\/span>se\u00e7\u00e3o transversal\u00a0 constante, <\/b><\/span><\/span><\/span>que possui\u00a0<\/b><\/span><\/span><\/span>massa (m)<\/b><\/span><\/span><\/span>\u00a0e\u00a0<\/b><\/span><\/span><\/span>comprimento (L),<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>\u00e0 express\u00e3o:<\/b><\/span><\/span><\/span><\/p>\n

Significado f\u00edsico de\u00a0\u00b5\u00a0\"\"<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>significa quanto <\/b><\/span><\/span><\/span>de <\/b><\/span><\/span><\/span>massa a corda tem por unidade de comprimento.<\/b><\/span><\/span><\/span> Assim, uma <\/b><\/span><\/span><\/span>corda de 0,5 kg\/m <\/b><\/span><\/span><\/span>possui, no SI, <\/b><\/span><\/span><\/span>0,5kg de massa para cada 1 metro de comprimento.<\/b><\/span><\/span><\/span>\"\"<\/p>\n

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

\"\"<\/p>\n

A <\/b><\/span><\/span><\/span>velocidade (V)<\/b><\/span><\/span><\/span>\u00a0de propaga\u00e7\u00e3o do pulso na corda \u00e9 dada, <\/b><\/span><\/span><\/span>tamb\u00e9m<\/b><\/span><\/span><\/span> <\/b>por:<\/b><\/span><\/span><\/span><\/p>\n

Onde <\/b><\/span><\/span><\/span>T \u00e9 a intensidade da for\u00e7a <\/b><\/span><\/span><\/span>que <\/b><\/span><\/span><\/span>traciona <\/b><\/span><\/span><\/span>(estica) <\/b><\/span><\/span><\/span>a corda e \u00b5 \u00e9 a densidade linear de massa da mesma.<\/b><\/span><\/span><\/span><\/p>\n

Observe que <\/b><\/span><\/span><\/span>V \u00e9 diretamente proporcional a\u00a0\"\", <\/b><\/span><\/span><\/span>ou seja, <\/b><\/span><\/span><\/span>quanto mais esticada estiver a corda, maior <\/b><\/span><\/span><\/span>ser\u00e1 a <\/b><\/span><\/span><\/span>velocidade de propaga\u00e7\u00e3o do pulso ou da onda na mesma <\/b><\/span><\/span><\/span>e que <\/b><\/span><\/span><\/span>V<\/b><\/span><\/span><\/span> \u00e9 <\/b><\/span><\/span><\/span>inversamente proporcional\u00a0 a\u00a0\"\", <\/b><\/span><\/span><\/span>ou seja, quanto <\/b><\/span><\/span><\/span>maior<\/b><\/span><\/span><\/span> a <\/b><\/span><\/span><\/span>densidade linear da corda, menor<\/b><\/span><\/span><\/span> ser\u00e1 a <\/b><\/span><\/span><\/span>velocidade de propaga\u00e7\u00e3o da onda na mesma.<\/b><\/span><\/span><\/span><\/p>\n

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

Podem ser de dois tipos:<\/b><\/span><\/span><\/span><\/p>\n

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

Ondas circulares (esf\u00e9ricas)<\/b><\/span><\/span><\/span>\u00a0\"\"<\/b><\/span><\/span><\/span> Quando a <\/b><\/span><\/span><\/span>ponta da r\u00e9gua bate continua e periodicamente <\/b><\/span><\/span><\/span>na <\/b><\/span><\/span><\/span>superf\u00edcie da \u00e1gua <\/b><\/span><\/span><\/span>origina <\/b><\/span><\/span><\/span>perturba\u00e7\u00f5es circulares <\/b><\/span><\/span><\/span>(ondas circulares) 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

A <\/b><\/span><\/span><\/span>frente de onda ou superf\u00edcie de onda <\/b><\/span><\/span><\/span>\u00e9 o <\/b><\/span><\/span><\/span>lugar geom\u00e9trico <\/b><\/span><\/span><\/span>de <\/b><\/span><\/span><\/span>todos os pontos <\/b><\/span><\/span><\/span>que est\u00e3o em <\/b><\/span><\/span><\/span>concord\u00e2ncia de fase de vibra\u00e7\u00e3o<\/b><\/span><\/span><\/span>, como por exemplo, <\/b><\/span><\/span><\/span>duas cristas ou dois vales.<\/b><\/span><\/span><\/span>\"\"<\/p>\n

O <\/b><\/span><\/span><\/span>raio de onda <\/b><\/span><\/span><\/span>\u00e9 toda <\/b><\/span><\/span><\/span>reta perpendicular \u00e0s frentes de onda <\/b><\/span><\/span><\/span>e que indicam a <\/b><\/span><\/span><\/span>dire\u00e7\u00e3o e o sentido de propaga\u00e7\u00e3o dessas ondas.<\/b><\/span><\/span><\/span><\/p>\n

O <\/b><\/span><\/span><\/span>comprimento de onda (\u03bb) <\/b><\/span><\/span><\/span>\u00e9 a <\/b><\/span><\/span><\/span>dist\u00e2ncia entre duas frentes de onda consecutivas.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

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

\"\"<\/p>\n

Ondas planas (retas)<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Produzidas <\/b><\/span><\/span><\/span>tocando-se leve e continuamente a superf\u00edcie da \u00e1gua com uma r\u00e9gua (fonte) na posi\u00e7\u00e3o indicada na figura.<\/b><\/span><\/span><\/span><\/p>\n

Observe que as <\/b><\/span><\/span><\/span>frentes de ondas e os raios de onda s\u00e3o retas paralelas e consequentemente perpendiculares.<\/b><\/span><\/span><\/span><\/p>\n

O <\/b><\/span><\/span><\/span>comprimento de onda (\u03bb)<\/b><\/span><\/span><\/span> \u00e9 a <\/b><\/span><\/span><\/span>dist\u00e2ncia entre duas frentes de onda (cristas ou vales) consecutivas.<\/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

Amplitude da onda (A)<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

\u00a0<\/span>Amplitude (A)<\/b><\/span><\/span><\/span>\u00a0\"\" corresponde \u00e0 <\/b><\/span><\/span><\/span>dist\u00e2ncia da ordenada (Y), <\/b><\/span><\/span><\/span>em m\u00f3dulo, <\/b><\/span><\/span><\/span>entre a parte mais alta<\/b><\/span><\/span><\/span> (crista) ou a <\/b><\/span><\/span><\/span>parte mais baixa <\/b><\/span><\/span><\/span>(vale) e o <\/b><\/span><\/span><\/span>ponto m\u00e9dio (0).<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Comprimento de onda (\u03bb)<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Representa <\/b><\/span><\/span><\/span>a <\/b><\/span><\/span><\/span>dist\u00e2ncia percorrida pela onda at\u00e9 come\u00e7ar novamente a repeti\u00e7\u00e3o<\/b><\/span><\/span><\/span>, ou seja, \u00e9 a <\/b><\/span><\/span><\/span>menor<\/b><\/span><\/span><\/span> <\/b>dist\u00e2ncia entre dois pontos consecutivos <\/b><\/span><\/span><\/span>que est\u00e3o em <\/b><\/span><\/span><\/span>concord\u00e2ncia de fase<\/b><\/span><\/span><\/span>, como por exemplo a <\/b><\/span><\/span><\/span>menor dist\u00e2ncia entre duas cristas ou dois vales.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Per\u00edodo (T)<\/b><\/span><\/span><\/span>\u00a0\"\"<\/b><\/span><\/span><\/span> <\/b>tempo que a onda demora para percorrer um comprimento de onda (1\u03bb), <\/b><\/span><\/span><\/span>que \u00e9 o <\/b><\/span><\/span><\/span>mesmo tempo que um ponto qualquer da onda demora para oscila\u00e7\u00e3o<\/b><\/span><\/span><\/span> (vai e vem) <\/b><\/span><\/span><\/span>completa<\/b><\/span><\/span><\/span> e que \u00e9 o <\/b><\/span><\/span><\/span>mesmo tempo que a fonte demora para gerar uma onda completa.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Freq\u00fc\u00eancia (f)<\/b><\/span><\/span><\/span>\u00a0\"\"<\/b><\/span><\/span><\/span> <\/b>representa quantas oscila\u00e7\u00f5es completas uma onda efetua em cada unidade de tempo, <\/b><\/span><\/span><\/span>ou ainda, <\/b><\/span><\/span><\/span>quantos comprimentos de onda completos passam por um ponto da onda em cada unidade de tempo.<\/b><\/span><\/span><\/span><\/p>\n

Se o <\/b><\/span><\/span><\/span>per\u00edodo T <\/b><\/span><\/span><\/span>estiver <\/b><\/span><\/span><\/span>em segundos (s) a freq\u00fc\u00eancia estar\u00e1 em hertz (Hz), <\/b><\/span><\/span><\/span>que significa <\/b><\/span><\/span><\/span>ciclos por segundo e a rela\u00e7\u00e3o entre f e T <\/b><\/span><\/span><\/span>est\u00e1 abaixo:<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

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

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

\"\"<\/p>\n

\"\"<\/p>\n

F\u00f3rmulas<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

Se o <\/b><\/span><\/span><\/span>meio \u00e9 o mesmo, V,\u00a0\u03bb\u00a0e f <\/b><\/span><\/span><\/span>tamb\u00e9m <\/b><\/span><\/span><\/span>s\u00e3o os mesmos.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

A <\/b><\/span><\/span><\/span>amplitude A n\u00e3o est\u00e1 relacionada com V, f e \u03bb, mas apenas com a quantidade de energia transportada <\/b><\/span><\/span><\/span>pela onda. <\/b><\/span><\/span><\/span>Quanto maior a energia, maior a amplitude e vice-versa.<\/b><\/span><\/span><\/span><\/p>\n

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

\"\"<\/p>\n

Ondas bidimensionais circulares<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

Ondas bidimensionais planas<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

Ondas em meios tridimensionais<\/b><\/span><\/span><\/span> A onda se <\/b><\/span><\/span><\/span>propaga no espa\u00e7o <\/b><\/span><\/span><\/span>e em <\/b><\/span><\/span><\/span>todas as dire\u00e7\u00f5es. <\/b><\/span><\/span><\/span>Exemplo: <\/b><\/span><\/span><\/span>Ondas sonoras e luz.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

As <\/b><\/span><\/span><\/span>frentes de onda s\u00e3o esferas e os raios de onda s\u00e3o radiais e saem da fonte de perturba\u00e7\u00e3o em todas as dire\u00e7\u00f5es.<\/b><\/span><\/span><\/span><\/p>\n

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

\"\" Exerc\u00edcios interessantes os quais voc\u00ea deve conferir:<\/b><\/span><\/span><\/span><\/p>\n

01-(FUVEST-SP)<\/b><\/span><\/span><\/span> <\/b>Num <\/b><\/span><\/span><\/span>lago<\/b><\/span><\/span><\/span> o <\/b><\/span><\/span><\/span>vento produz ondas peri\u00f3dicas <\/b><\/span><\/span><\/span>que se <\/b><\/span><\/span><\/span>propagam<\/b><\/span><\/span><\/span> com a <\/b><\/span><\/span><\/span>velocidade<\/b><\/span><\/span><\/span><\/p>\n

de 2m\/s. <\/b><\/span><\/span><\/span>O <\/b><\/span><\/span><\/span>comprimento de onda \u00e9 10m. <\/b><\/span><\/span><\/span>Determine o <\/b><\/span><\/span><\/span>per\u00edodo de oscila\u00e7\u00e3o de um barco:<\/b><\/span><\/span><\/span>\"\"<\/p>\n

a) <\/b><\/span><\/span><\/span>quando <\/b><\/span><\/span><\/span>ancorado nesse lago.<\/b><\/span><\/span><\/span><\/p>\n

b) <\/b><\/span><\/span><\/span>quando se <\/b><\/span><\/span><\/span>movimenta em sentido contr\u00e1rio ao da propaga\u00e7\u00e3o das ondas<\/b><\/span><\/span><\/span>, com uma <\/b><\/span><\/span><\/span>velocidade de 8m\/s.<\/b><\/span><\/span><\/span><\/p>\n

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

a) Com o barco ancorado (parado) \"\" V = 2 m\/s \"\" \u03bb = 10 m \"\" equa\u00e7\u00e3o fundamental da ondulat\u00f3ria\"\" V = \u03bb.f\u00a0 \"\"<\/b><\/span><\/span><\/span>\u00a0 2 = 10.f\u00a0 \"\"\u00a0 <\/b><\/span><\/span><\/span>f = 0,2 Hz\u00a0 \"\"<\/b><\/span><\/span><\/span>\u00a0 <\/b><\/span><\/span><\/span>T = 1\/f\u00a0 \"\"<\/b><\/span><\/span><\/span>\u00a0 T = 1\/0,2\u00a0 \"\"\u00a0\u00a0<\/b><\/span><\/span><\/span>T = 5 s.<\/b><\/span><\/span><\/span><\/p>\n

b) <\/b><\/span><\/span><\/span>Como se <\/b><\/span><\/span><\/span>movem em sentido contr\u00e1rio <\/b><\/span><\/span><\/span>a <\/b><\/span><\/span><\/span>velocidade relativa entre o barco e a onda <\/b><\/span><\/span><\/span>\u00e9 de <\/b><\/span><\/span><\/span>V = 2 + 8<\/b><\/span><\/span><\/span>\u00a0 \"\"\u00a0 <\/b><\/span><\/span><\/span>V = 10 m\/s.<\/b><\/span><\/span><\/span>\"\"<\/p>\n

O comprimento de onda continua o mesmo \u03bb = 10 m = \u0394S \"\" ent\u00e3o, para percorrer \u0394S = \u03bb = 10 m a onda deve demorar o tempo de um per\u00edodo \u0394t = T com velocidade de V = 10 m\/s <\/b><\/span><\/span><\/span>\u00a0\"\"\u00a0\u00a0<\/b><\/span><\/span><\/span>V = \u0394S\/\u0394t\u00a0 \"\"<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span><\/p>\n

10 = 10\/T\u00a0 \"\"\u00a0\u00a0<\/b><\/span><\/span><\/span>T = 1 s.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

\u00a0Utilizando a <\/b><\/span><\/span><\/span>express\u00e3o fornecida V = \"\" :<\/b><\/span><\/span><\/span><\/p>\n

Na parte mais rasa \"\" V<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span> = \"\" \"\" V<\/b><\/span><\/span><\/span>1 <\/b><\/span><\/span><\/sub><\/span>= 5 m\/s.<\/b><\/span><\/span><\/span>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <\/b><\/span><\/span><\/span><\/p>\n

Na parte mais profunda\u00a0 \"\"<\/b><\/span><\/span><\/span>\u00a0 <\/b><\/span><\/span><\/span>V<\/b><\/span><\/span><\/span>2 \"\" <\/b><\/span><\/span><\/sub><\/span>\u00a0 \"\"\u00a0 <\/b><\/span><\/span><\/span>V<\/b><\/span><\/span><\/span>2 <\/b><\/span><\/span><\/sub><\/span>= 10 m\/s.<\/b><\/span><\/span><\/span><\/p>\n

Como, pelo enunciado a <\/b><\/span><\/span><\/span>frequ\u00eancia f \u00e9 a mesma <\/b><\/span><\/span><\/span> \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>.f\u00a0 \"\"<\/b><\/span><\/span><\/span>\u00a0 5 = \u03bb<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>.f\u00a0 \"\" <\/b><\/span><\/span><\/span>f = 5\/\u03bb<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span> (I) \"\" V<\/b><\/span><\/span><\/span>2 <\/b><\/span><\/span><\/sub><\/span>= \u03bb<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span>.f\u00a0 \"\"<\/b><\/span><\/span><\/span>\u00a0 10 = \u03bb<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span>.f\u00a0 \"\" <\/b><\/span><\/span><\/span>f = 10\/\u03bb<\/b><\/span><\/span><\/span>2 <\/b><\/span><\/span><\/sub><\/span>(II).<\/b><\/span><\/span><\/span><\/p>\n

Igualando (I) com (II) \"\" <\/b><\/span><\/span><\/span>5\/<\/b><\/span><\/span><\/span>\u03bb<\/b><\/span><\/span><\/span><\/span>1 <\/b><\/span><\/span><\/sub><\/span>= 10\/<\/b><\/span><\/span><\/span>\u03bb<\/b><\/span><\/span><\/span><\/span>2\u00a0<\/b><\/span><\/span><\/sub><\/span>\u00a0\u00a0\"\" \u00a0<\/b><\/span><\/span><\/span>5<\/b><\/span><\/span><\/span>\u03bb<\/b><\/span><\/span><\/span>2 <\/b><\/span><\/span><\/sub><\/span>= 10\u03bb<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span> \"\"<\/b><\/span><\/span><\/span> <\/b>\u03bb<\/b><\/span><\/span><\/span>2 <\/b><\/span><\/span><\/sub><\/span>= 2\u03bb<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>. <\/b><\/span><\/span><\/span><\/p>\n

R – B\u00a0<\/b><\/span><\/span><\/span><\/p>\n

03-(UNICAMP-SP)<\/b><\/span><\/span><\/span> <\/b>O <\/b><\/span><\/span><\/span>sistema GPS (“Global Positioning System”) <\/b><\/span><\/span><\/span>consiste em um <\/b><\/span><\/span><\/span>conjunto de sat\u00e9lites em \u00f3rbita em torno da Terra <\/b><\/span><\/span><\/span>que <\/b><\/span><\/span><\/span>transmitem sinais eletromagn\u00e9ticos <\/b><\/span><\/span><\/span>para <\/b><\/span><\/span><\/span>receptores <\/b><\/span><\/span><\/span>na <\/b><\/span><\/span><\/span>superf\u00edcie terrestre. <\/b><\/span><\/span><\/span><\/p>\n

A <\/b><\/span><\/span><\/span>velocidade de propaga\u00e7\u00e3o <\/b><\/span><\/span><\/span>dos sinais \u00e9 de <\/b><\/span><\/span><\/span>300.000 km\/s. <\/b><\/span><\/span><\/span>Para que o <\/b><\/span><\/span><\/span>sistema funcione bem<\/b><\/span><\/span><\/span>, a <\/b><\/span><\/span><\/span>absor\u00e7\u00e3o atmosf\u00e9rica desse sinal eletromagn\u00e9tico deve ser pequena<\/b><\/span><\/span><\/span>. <\/b><\/span><\/span><\/span><\/p>\n

A <\/b><\/span><\/span><\/span>figura a seguir <\/b><\/span><\/span><\/span>mostra a <\/b><\/span><\/span><\/span>porcentagem de radia\u00e7\u00e3o eletromagn\u00e9tica absorvida pela atmosfera em fun\u00e7\u00e3o do comprimento de onda.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

a) <\/b><\/span><\/span><\/span>A <\/b><\/span><\/span><\/span>freq\u00fc\u00eancia do sinal GPS <\/b><\/span><\/span><\/span>\u00e9 igual a <\/b><\/span><\/span><\/span>1.500 MHz. <\/b><\/span><\/span><\/span>Qual o <\/b><\/span><\/span><\/span>comprimento de onda correspondente?<\/b><\/span><\/span><\/span> Qual a <\/b><\/span><\/span><\/span>porcentagem de absor\u00e7\u00e3o do sinal pela atmosfera?<\/b><\/span><\/span><\/span><\/p>\n

b) <\/b><\/span><\/span><\/span>Uma das <\/b><\/span><\/span><\/span>aplica\u00e7\u00f5es mais importantes do sistema GPS <\/b><\/span><\/span><\/span>\u00e9 a <\/b><\/span><\/span><\/span>determina\u00e7\u00e3o da posi\u00e7\u00e3o<\/b><\/span><\/span><\/span> de um certo <\/b><\/span><\/span><\/span>receptor na Terra. <\/b><\/span><\/span><\/span><\/p>\n

Essa <\/b><\/span><\/span><\/span>determina\u00e7\u00e3o<\/b><\/span><\/span><\/span> \u00e9 <\/b><\/span><\/span><\/span>feita atrav\u00e9s da medida do tempo <\/b><\/span><\/span><\/span>que o sinal <\/b><\/span><\/span><\/span>leva para ir do sat\u00e9lite at\u00e9 <\/b><\/span><\/span><\/span>o <\/b><\/span><\/span><\/span>receptor.<\/b><\/span><\/span><\/span> <\/b><\/p>\n

Qual \u00e9 a <\/b><\/span><\/span><\/span>varia\u00e7\u00e3o\u00a0\u0394t na medida do tempo <\/b><\/span><\/span><\/span>feita pelo <\/b><\/span><\/span><\/span>receptor<\/b><\/span><\/span><\/span> que <\/b><\/span><\/span><\/span>corresponde a uma varia\u00e7\u00e3o <\/b><\/span><\/span><\/span>na <\/b><\/span><\/span><\/span>dist\u00e2ncia sat\u00e9lite-receptor de\u00a0\u0394x = 100m? <\/b><\/span><\/span><\/span>Considere\u00a0que a <\/b><\/span><\/span><\/span>trajet\u00f3ria do sinal seja retil\u00ednea.<\/b><\/span><\/span><\/span><\/p>\n

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

a) <\/b><\/span><\/span><\/span>S\u00e3o dados \"\"<\/b><\/span><\/span><\/span> V = 300.000 km\/s = 3.10<\/b><\/span><\/span><\/span>8<\/b><\/span><\/span><\/sup><\/span> m\/s e f = 1.500MHz = 1500.10<\/b><\/span><\/span><\/span>6<\/b><\/span><\/span><\/sup><\/span> Hz.<\/b><\/span><\/span><\/span><\/p>\n

Aplicando a<\/b><\/span><\/span><\/span> equa\u00e7\u00e3o fundamental da ondulat\u00f3ria V = \u03bbf \"\"<\/b><\/span><\/span><\/span>\u00a0\u00a0 3.10<\/b><\/span><\/span><\/span>8 <\/b><\/span><\/span><\/sup><\/span>= \u03bb.1.500.10<\/b><\/span><\/span><\/span>6 <\/b><\/span><\/span><\/sup><\/span>\u00a0\"\" \u00a0<\/b><\/span><\/span><\/span>\u03bb<\/b><\/span><\/span><\/span> = 2,0.10<\/b><\/span><\/span><\/span>-1<\/b><\/span><\/span><\/sup><\/span>m.<\/b><\/span><\/span><\/span><\/p>\n

Veja pelo <\/b><\/span><\/span><\/span>gr\u00e1fico <\/b><\/span><\/span><\/span>que para esse <\/b><\/span><\/span><\/span>comprimento de onda <\/b><\/span><\/span><\/span>(<\/b><\/span><\/span><\/span>\u03bb<\/b><\/span><\/span><\/span> = 2,0.10<\/b><\/span><\/span><\/span>-1<\/b><\/span><\/span><\/sup><\/span>m)<\/b><\/span><\/span><\/span>, <\/b><\/span><\/span><\/span>a<\/b><\/span><\/span><\/span> porcentagem (fra\u00e7\u00e3o) de absor\u00e7\u00e3o do sinal pela atmosfera \u00e9 nula<\/b><\/span><\/span><\/span><\/p>\n

b)\u00a0 <\/b><\/span><\/span><\/span><\/span>\u0394<\/b><\/span><\/span><\/span>x = <\/b><\/span><\/span><\/span><\/span>\u0394<\/b><\/span><\/span><\/span>S =100m \"\" V = <\/b><\/span><\/span><\/span><\/span>\u0394<\/b><\/span><\/span><\/span>S\/<\/b><\/span><\/span><\/span><\/span>\u0394<\/b><\/span><\/span><\/span>t\u00a0<\/b><\/span><\/span><\/span><\/span> \"\"\u00a0 3.10<\/b><\/span><\/span><\/span><\/span>8 <\/b><\/span><\/span><\/span><\/sup><\/span>= 100\/<\/b><\/span><\/span><\/span><\/span>\u0394<\/b><\/span><\/span><\/span>t\u00a0 \"\"\u00a0\u00a0<\/b><\/span><\/span><\/span><\/span>\u0394<\/b><\/span><\/span><\/span>t = 3,3.10<\/b><\/span><\/span><\/span><\/span>-7<\/b><\/span><\/span><\/span><\/sup><\/span>\u00a0s<\/b><\/span><\/span><\/span><\/span><\/p>\n

04-(FUVEST-SP)<\/b><\/span><\/span><\/span> <\/b>Um <\/b><\/span><\/span><\/span>sensor,<\/b><\/span><\/span><\/span> montado em uma <\/b><\/span><\/span><\/span>plataforma da Petrobr\u00e1s, <\/b><\/span><\/span><\/span>com <\/b><\/span><\/span><\/span>posi\u00e7\u00e3o fixa <\/b><\/span><\/span><\/span>em <\/b><\/span><\/span><\/span>rela\u00e7\u00e3o ao fundo do mar, <\/b><\/span><\/span><\/span>registra as <\/b><\/span><\/span><\/span>sucessivas posi\u00e7\u00f5es de uma pequena bola <\/b><\/span><\/span><\/span>que <\/b><\/span><\/span><\/span>flutua<\/b><\/span><\/span><\/span> sobre a <\/b><\/span><\/span><\/span>superf\u00edcie da \u00e1gua,<\/b><\/span><\/span><\/span> \u00e0 medida que uma <\/b><\/span><\/span><\/span>onda do mar passa por essa bola continuamente.<\/b><\/span><\/span><\/span> <\/b><\/p>\n

A <\/b><\/span><\/span><\/span>bola descreve um movimento aproximadamente circular, <\/b><\/span><\/span><\/span>no <\/b><\/span><\/span><\/span>plano vertical, <\/b><\/span><\/span><\/span>mantendo-se em torno da <\/b><\/span><\/span><\/span>mesma posi\u00e7\u00e3o m\u00e9dia<\/b><\/span><\/span><\/span>, tal como reproduzido na <\/b><\/span><\/span><\/span>seq\u00fc\u00eancia de registros adiante<\/b><\/span><\/span><\/span>, nos <\/b><\/span><\/span><\/span>tempos indicados. <\/b><\/span><\/span><\/span>O <\/b><\/span><\/span><\/span>intervalo entre registros \u00e9 menor do que o per\u00edodo da onda.<\/b><\/span><\/span><\/span> <\/b><\/p>\n

A <\/b><\/span><\/span><\/span>velocidade de propaga\u00e7\u00e3o <\/b><\/span><\/span><\/span>dessa <\/b><\/span><\/span><\/span>onda senoidal \u00e9 de 1,5 m\/s.<\/b><\/span><\/span><\/span><\/p>\n

Para <\/b><\/span><\/span><\/span>essas condi\u00e7\u00f5es:<\/b><\/span><\/span><\/span>\"\"<\/p>\n

a)<\/b><\/span><\/span><\/span> <\/b>Determine o <\/b><\/span><\/span><\/span>per\u00edodo T, <\/b><\/span><\/span><\/span>em <\/b><\/span><\/span><\/span>segundos,<\/b><\/span><\/span><\/span> dessa <\/b><\/span><\/span><\/span>onda do mar.<\/b><\/span><\/span><\/span><\/p>\n

b)<\/b><\/span><\/span><\/span> <\/b>Determine o <\/b><\/span><\/span><\/span>comprimento de onda \"\", <\/b><\/span><\/span><\/span>em <\/b><\/span><\/span><\/span>m, <\/b><\/span><\/span><\/span>dessa <\/b><\/span><\/span><\/span>onda do mar.<\/b><\/span><\/span><\/span><\/p>\n

c)<\/b><\/span><\/span><\/span> <\/b>Represente, um <\/b><\/span><\/span><\/span>esquema do perfil dessa onda, <\/b><\/span><\/span><\/span>para o <\/b><\/span><\/span><\/span>instante t = 14 s, <\/b><\/span><\/span><\/span>tal como <\/b><\/span><\/span><\/span>visto da plataforma fixa.<\/b><\/span><\/span><\/span> Indique os <\/b><\/span><\/span><\/span>valores apropriados nos eixos horizontal e vertical.<\/b><\/span><\/span><\/span><\/p>\n

Resolu\u00e7\u00e3o:<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span><\/p>\n

a)<\/b><\/span><\/span><\/span> <\/b>Trata-se de uma <\/b><\/span><\/span><\/span>onda mista, <\/b><\/span><\/span><\/span>pois <\/b><\/span><\/span><\/span>oscila na horizontal e na vertical<\/b><\/span><\/span><\/span> e estas <\/b><\/span><\/span><\/span>oscila\u00e7\u00f5es<\/b><\/span><\/span><\/span> numa <\/b><\/span><\/span><\/span>onda mista ocorrem no mesmo tempo nestas duas dire\u00e7\u00f5es.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Observe <\/b><\/span><\/span><\/span>nas figuras acima<\/b><\/span><\/span><\/span>, que o <\/b><\/span><\/span><\/span>intervalo de tempo de 6s <\/b><\/span><\/span><\/span>corresponde a <\/b><\/span><\/span><\/span>tr\u00eas quartos do per\u00edodo T, <\/b><\/span><\/span><\/span>ou seja, <\/b><\/span><\/span><\/span>T=8s.<\/b><\/span><\/span><\/span><\/p>\n

b)<\/b><\/span><\/span><\/span> f=1\/T\u00a0 \"\"<\/b><\/span><\/span><\/span>\u00a0 <\/b><\/span><\/span><\/span>f = (1\/8) Hz\u00a0 \"\"<\/b><\/span><\/span><\/span>\u00a0 <\/b><\/span><\/span><\/span>V = \u03bb.f\u00a0 \"\"<\/b><\/span><\/span><\/span>\u00a0 1,5 = \u03bb.(1\/8) \u00a0\"\"\u00a0\u00a0<\/b><\/span><\/span><\/span>\u03bb = 12 m.<\/b><\/span><\/span><\/span><\/p>\n

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

\"\"<\/p>\n

05-(UFRJ-RJ)<\/b><\/span><\/span><\/span> <\/b>Atrav\u00e9s de um <\/b><\/span><\/span><\/span>dispositivo adequado<\/b><\/span><\/span><\/span> produzem-se <\/b><\/span><\/span><\/span>ondas em um meio el\u00e1stico, <\/b><\/span><\/span><\/span>de tal modo que as <\/b><\/span><\/span><\/span>freq\u00fc\u00eancias das ondas obtidas se encontram no intervalo de 15Hz a 60Hz.<\/b><\/span><\/span><\/span> O gr\u00e1fico mostra como varia o comprimento de onda (\u03bb) em fun\u00e7\u00e3o da freq\u00fc\u00eancia (f).<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

a)<\/b><\/span><\/span><\/span> Calcule o <\/b><\/span><\/span><\/span>menor comprimento de onda produzido nessa experi\u00eancia.<\/b><\/span><\/span><\/span><\/p>\n

b)<\/b><\/span><\/span><\/span> <\/b>Para um <\/b><\/span><\/span><\/span>comprimento de onda de 12m, calcule o per\u00edodo da onda.<\/b><\/span><\/span><\/span><\/p>\n

Resolu\u00e7\u00e3o:<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span><\/p>\n

a) <\/b><\/span><\/span><\/span>Quando<\/b><\/span><\/span><\/span> f = 30 Hz, \u03bb = 12 m \"\" equa\u00e7\u00e3o fundamental da ondulat\u00f3ria \"\" V =\"\".f\u00a0 \"\"<\/b><\/span><\/span><\/span>\u00a0 <\/b><\/span><\/span><\/span>V = 12.30\u00a0 \"\"<\/b><\/span><\/span><\/span><\/p>\n

\u00a0 <\/span>V = 360m\/s<\/b><\/span><\/span><\/span> <\/b>(constante-mesmo meio).<\/b><\/span><\/span><\/span><\/p>\n

O <\/b><\/span><\/span><\/span>menor\u00a0\u03bb<\/b><\/span><\/span><\/span>\u00a0ocorre quando <\/b><\/span><\/span><\/span>f = 60 Hz (vide gr\u00e1fico)\u00a0 \"\"<\/b><\/span><\/span><\/span>\u00a0 360 = \u03bb.60\u00a0 \"\"\u00a0\u00a0<\/b><\/span><\/span><\/span>\u03bb<\/b><\/span><\/span><\/span>m\u00ednimo <\/b><\/span><\/span><\/sub><\/span>= 6 m.<\/b><\/span><\/span><\/span><\/p>\n

b)<\/b><\/span><\/span><\/span> <\/b>Quando\u00a0<\/b><\/span><\/span><\/span>\u03bb = 12 m, f = 30 Hz\u00a0 \"\"<\/b><\/span><\/span><\/span>\u00a0 <\/b><\/span><\/span><\/span>T = 1\/f\u00a0 \"\"<\/b><\/span><\/span><\/span>\u00a0\u00a0<\/b><\/span><\/span><\/span>T = (1\/30) s.<\/b><\/span><\/span><\/span><\/p>\n

06-(FUVEST-SP)<\/b><\/span><\/span><\/span> <\/b>Um <\/b><\/span><\/span><\/span>grande aqu\u00e1rio, <\/b><\/span><\/span><\/span>com <\/b><\/span><\/span><\/span>paredes laterais de vidro,<\/b><\/span><\/span><\/span> permite <\/b><\/span><\/span><\/span>visualizar,<\/b><\/span><\/span><\/span> na <\/b><\/span><\/span><\/span>superf\u00edcie da \u00e1gua, uma onda que se propaga.<\/b><\/span><\/span><\/span> <\/b><\/p>\n

A <\/b><\/span><\/span><\/span>figura<\/b><\/span><\/span><\/span> representa o <\/b><\/span><\/span><\/span>perfil de tal onda no instante T<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sub><\/span>. Durante <\/b><\/span><\/span><\/span>sua passagem,<\/b><\/span><\/span><\/span> uma <\/b><\/span><\/span><\/span>b\u00f3ia,<\/b><\/span><\/span><\/span> em dada <\/b><\/span><\/span><\/span>posi\u00e7\u00e3o,<\/b><\/span><\/span><\/span> <\/b>oscila para cima e para baixo <\/b><\/span><\/span><\/span>e seu <\/b><\/span><\/span><\/span>deslocamento vertical (y), <\/b><\/span><\/span><\/span>em <\/b><\/span><\/span><\/span>fun\u00e7\u00e3o<\/b><\/span><\/span><\/span> do <\/b><\/span><\/span><\/span>tempo,<\/b><\/span><\/span><\/span> est\u00e1 representado no gr\u00e1fico<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Calcule,<\/b><\/span><\/span><\/span> com essas <\/b><\/span><\/span><\/span>informa\u00e7\u00f5es,<\/b><\/span><\/span><\/span> a <\/b><\/span><\/span><\/span>velocidade de propaga\u00e7\u00e3o da onda.<\/b><\/span><\/span><\/span><\/p>\n

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

Da figura, o <\/b><\/span><\/span><\/span>comprimento de onda \u03bb <\/b><\/span><\/span><\/span>pode ser a <\/b><\/span><\/span><\/span>dist\u00e2ncia entre duas cristas sucessivas\u00a0 \"\" \u03bb = 20 m.<\/b><\/span><\/span><\/span><\/p>\n

Do gr\u00e1fico, o <\/b><\/span><\/span><\/span>per\u00edodo T \u00e9 o intervalo de tempo que a onda demora para come\u00e7ar a repeti\u00e7\u00e3o\u00a0 \"\" T = <\/b><\/span><\/span><\/span><\/p>\n

10 s \"\" <\/b><\/span><\/span><\/span>f = 1\/T\u00a0 \"\" <\/b><\/span><\/span><\/span>f = (1\/10) Hz.<\/b><\/span><\/span><\/span><\/p>\n

Equa\u00e7\u00e3o fundamental da ondulat\u00f3ria\u00a0 \"\" V = \u03bb.f\u00a0\u00a0\"\"<\/b><\/span><\/span><\/span>\u00a0\u00a0V =20.(1\/10)\u00a0 \"\"\u00a0\u00a0<\/b><\/span><\/span><\/span>V = 2,0m\/s.<\/b><\/span><\/span><\/span><\/p>\n

 <\/p>\n

Confira os exerc\u00edcios com resolu\u00e7\u00f5es comentadas<\/span><\/a><\/h3>\n","protected":false},"excerpt":{"rendered":"

Equa\u00e7\u00e3o da onda (Equa\u00e7\u00e3o fundamental da ondulat\u00f3ria) Elementos de uma onda Considere a onda peri\u00f3dica (sucess\u00e3o de pulsos iguais em tempos iguais) das figurasa seguir, cujas principais caracter\u00edsticas s\u00e3o: \u00a0 Comprimento de onda (\u03bb)\u00a0 representa a dist\u00e2ncia percorrida pela onda at\u00e9 come\u00e7ar novamente a repeti\u00e7\u00e3o, ou seja, \u00e9 a menor dist\u00e2ncia entre dois pontos consecutivos que est\u00e3o em concor-d\u00e2ncia de<\/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-2428","page","type-page","status-publish","hentry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/2428","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=2428"}],"version-history":[{"count":2,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/2428\/revisions"}],"predecessor-version":[{"id":2437,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/2428\/revisions\/2437"}],"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=2428"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}