{"id":2419,"date":"2016-09-11T00:28:04","date_gmt":"2016-09-11T00:28:04","guid":{"rendered":"http:\/\/fisicaevestibular.com.br\/novo\/?page_id=2419"},"modified":"2024-08-23T15:06:07","modified_gmt":"2024-08-23T15:06:07","slug":"interferencia-de-ondas","status":"publish","type":"page","link":"https:\/\/fisicaevestibular.com.br\/novo\/ondulatoria\/ondas\/interferencia-de-ondas\/","title":{"rendered":"Interfer\u00eancia de Ondas"},"content":{"rendered":"

Interfer\u00eancia de Ondas<\/span><\/span><\/span><\/p>\n

Interfer\u00eancia de ondas em meios unidimensionais<\/b><\/span><\/span><\/span><\/p>\n

Considere <\/b><\/span><\/span><\/span>dois pulsos propagando-se<\/b><\/span><\/span><\/span> numa <\/b><\/span><\/span><\/span>mesma corda em sentidos opostos. <\/b><\/span><\/span><\/span><\/p>\n

Ao se <\/b><\/span><\/span><\/span>encontrarem ocorre a interfer\u00eancia <\/b><\/span><\/span><\/span>e no <\/b><\/span><\/span><\/span>encontro <\/b><\/span><\/span><\/span>ocorre o<\/b><\/span><\/span><\/span> fen\u00f4meno da superposi\u00e7\u00e3o <\/b><\/span><\/span><\/span>e nele, <\/b><\/span><\/span><\/span>cada ponto da corda corresponde \u00e0 soma das perturba\u00e7\u00f5es que seriam causadas por cada onda separadamente.<\/b><\/span><\/span><\/span><\/p>\n

Ap\u00f3s a <\/b><\/span><\/span><\/span>interfer\u00eancia<\/b><\/span><\/span><\/span> (cruzamento), <\/b><\/span><\/span><\/span>cada pulso continua seu caminho como se nada tivesse acontecido.<\/b><\/span><\/span><\/span><\/p>\n

\"\" Se os <\/b><\/span><\/span><\/span>pulsos tiverem a mesma amplitude<\/b><\/span><\/span><\/span> e a <\/b><\/span><\/span><\/span>mesma fase <\/b><\/span><\/span><\/span>teremos <\/b><\/span><\/span><\/span>interfer\u00eancia construtiva<\/b><\/span><\/span><\/span>.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

\"\" Se os <\/b><\/span><\/span><\/span>pulsos tiverem a mesma amplitude <\/b><\/span><\/span><\/span>e em <\/b><\/span><\/span><\/span>oposi\u00e7\u00e3o de fase <\/b><\/span><\/span><\/span>teremos\u00a0<\/b><\/span><\/span><\/span>interfer\u00eancia destrutiva.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

\"\" Se as <\/b><\/span><\/span><\/span>amplitudes forem diferentes <\/b><\/span><\/span><\/span>e tiverem <\/b><\/span><\/span><\/span>mesma fase<\/b><\/span><\/span><\/span> teremos\u00a0<\/b><\/span><\/span><\/span>interfer\u00eancia construtiva:<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

\"\" Se as <\/b><\/span><\/span><\/span>amplitudes forem diferentes <\/b><\/span><\/span><\/span>e estiverem em <\/b><\/span><\/span><\/span>oposi\u00e7\u00e3o de fase <\/b><\/span><\/span><\/span>teremos uma\u00a0<\/b><\/span><\/span><\/span>interfer\u00eancia destrutiva.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Interfer\u00eancia em meios bi e tri dimensionais<\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

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

\"\" Procure <\/b><\/span><\/span><\/span>entender e memorizar <\/b><\/span><\/span><\/span>os <\/b><\/span><\/span><\/span>casos de interfer\u00eancias <\/b><\/span><\/span><\/span>fornecidos na <\/b><\/span><\/span><\/span>teoria acima.<\/b><\/span><\/span><\/span><\/p>\n

\"\" Quando <\/b><\/span><\/span><\/span>duas ou mais ondas sofrem superposi\u00e7\u00e3o<\/b><\/span><\/span><\/span> temos o <\/b><\/span><\/span><\/span>fen\u00f4meno da interfer\u00eancia<\/b><\/span><\/span><\/span>, que <\/b><\/span><\/span><\/span>ocorre tanto para ondas transversais como para ondas longitudinais.<\/b><\/span><\/span><\/span><\/p>\n

\"\" Durante<\/b><\/span><\/span><\/span> a <\/b><\/span><\/span><\/span>superposi\u00e7\u00e3o<\/b><\/span><\/span><\/span>, a <\/b><\/span><\/span><\/span>amplitude da onda resultante <\/b><\/span><\/span><\/span>\u00e9 a <\/b><\/span><\/span><\/span>soma alg\u00e9brica <\/b><\/span><\/span><\/span>das <\/b><\/span><\/span><\/span>amplitudes de cada onda.<\/b><\/span><\/span><\/span><\/p>\n

\"\" Quando os <\/b><\/span><\/span><\/span>pulsos tiverem a mesma amplitude <\/b><\/span><\/span><\/span>e em <\/b><\/span><\/span><\/span>oposi\u00e7\u00e3o de fase teremosinterfer\u00eancia destrutiva<\/b><\/span><\/span><\/span>\u00a0e <\/b><\/span><\/span><\/span>durante a interfer\u00eancia, quando a corda estiver na horizontal, cada ponto da<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

mesma ter\u00e1 velocidade vertical e horizontal nulas.<\/b><\/span><\/span><\/span><\/p>\n

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

\"\" Nos <\/b><\/span><\/span><\/span>pres\u00eddios,<\/b><\/span><\/span><\/span> a <\/b><\/span><\/span><\/span>necessidade de se impossibilitar <\/b><\/span><\/span><\/span>qualquer tipo de <\/b><\/span><\/span><\/span>comunica\u00e7\u00e3o,<\/b><\/span><\/span><\/span> no caso de <\/b><\/span><\/span><\/span>organiza\u00e7\u00f5es criminosas, tornou-se patente. <\/b><\/span><\/span><\/span><\/p>\n

Embora <\/b><\/span><\/span><\/span>existam muitos sistemas de comunica\u00e7\u00e3o m\u00f3vel, <\/b><\/span><\/span><\/span>o <\/b><\/span><\/span><\/span>foco centrou-se em celulares, <\/b><\/span><\/span><\/span>em virtude de suas <\/b><\/span><\/span><\/span>pequenas dimens\u00f5es f\u00edsicas <\/b><\/span><\/span><\/span>e da <\/b><\/span><\/span><\/span>facilidade de aquisi\u00e7\u00e3o e uso.<\/b><\/span><\/span><\/span><\/p>\n

Uma das <\/b><\/span><\/span><\/span>propostas \u00e9 utilizar um aparelho <\/b><\/span><\/span><\/span>que origine <\/b><\/span><\/span><\/span>ondas eletromagn\u00e9ticas <\/b><\/span><\/span><\/span>na <\/b><\/span><\/span><\/span>mesma faixa <\/b><\/span><\/span><\/span>de <\/b><\/span><\/span><\/span>freq\u00fc\u00eancia utilizada <\/b><\/span><\/span><\/span>pelas <\/b><\/span><\/span><\/span>operadoras de telefonia m\u00f3vel. <\/b><\/span><\/span><\/span><\/p>\n

Essas <\/b><\/span><\/span><\/span>ondas ser\u00e3o espalhadas <\/b><\/span><\/span><\/span>por <\/b><\/span><\/span><\/span>meio de antenas,<\/b><\/span><\/span><\/span> normalmente <\/b><\/span><\/span><\/span>instaladas<\/b><\/span><\/span><\/span> nos <\/b><\/span><\/span><\/span>muros do pres\u00eddio.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Essas <\/b><\/span><\/span><\/span>ondas seriam emitidas nas mesmas freq\u00fc\u00eancias <\/b><\/span><\/span><\/span>utilizadas pelas <\/b><\/span><\/span><\/span>operadoras de telefonia m\u00f3vel.<\/b><\/span><\/span><\/span> <\/b><\/p>\n

Com isso, <\/b><\/span><\/span><\/span>atrav\u00e9s de\u00a0interfer\u00eancias destrutivas, compromete-se <\/b><\/span><\/span><\/span>a <\/b><\/span><\/span><\/span>comunica\u00e7\u00e3o entre a ERB (torre celular ou esta\u00e7\u00e3o de r\u00e1dio) e o telefone. (Ueg).<\/b><\/span><\/span><\/span><\/p>\n

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

Determinando o tipo de interfer\u00eancia num ponto P sob influ\u00eancia de duas fontes de ondas<\/b><\/span><\/span><\/span><\/p>\n

Condi\u00e7\u00f5es <\/b><\/span><\/span><\/span>para que um <\/b><\/span><\/span><\/span>ponto P <\/b><\/span><\/span><\/span>de um meio, <\/b><\/span><\/span><\/span>devido \u00e0 interfer\u00eancia de duas ondas <\/b><\/span><\/span><\/span>esteja em <\/b><\/span><\/span><\/span>interfer\u00eancia construtiva (refor\u00e7o) ou interfer\u00eancia destrutiva (aniquila\u00e7\u00e3o).<\/b><\/span><\/span><\/span><\/p>\n

\u00a0I<\/b><\/span><\/span><\/span> \"\" <\/b><\/span><\/span><\/span> <\/b>Meio unidimensional<\/b><\/span><\/span><\/span><\/p>\n

Considere <\/b><\/span><\/span><\/span>duas fontes F<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>\u00a0e F<\/b><\/span><\/span><\/span>2\u00a0<\/b><\/span><\/span><\/sub><\/span>produzindo no mesmo meio, ondas de mesma freq\u00fc\u00eancia (f), <\/b><\/span><\/span><\/span>mesmo <\/b><\/span><\/span><\/span>comprimento de onda (\u03bb), mesma amplitude A, em fase e se interferindo. <\/b><\/span><\/span><\/span><\/p>\n

O <\/b><\/span><\/span><\/span>ponto P \u00e9 distante d<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>\u00a0de F<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>\u00a0e d<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span>\u00a0de F<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span>.<\/b><\/span><\/span><\/span><\/p>\n

Devido <\/b><\/span><\/span><\/span>\u00e0 interfer\u00eancia <\/b><\/span><\/span><\/span>das <\/b><\/span><\/span><\/span>ondas geradas por essas duas fontes,<\/b><\/span><\/span><\/span> podem ocorrer <\/b><\/span><\/span><\/span>duas situa\u00e7\u00f5es particulares:<\/b><\/span><\/span><\/span><\/p>\n

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

1<\/b><\/span><\/span><\/span>a<\/b><\/span><\/span><\/sup><\/span>\u00a0\"\"<\/b><\/span><\/span><\/span> O <\/b><\/span><\/span><\/span>ponto P fica em repouso <\/b><\/span><\/span><\/span>(interfer\u00eancia destrutiva), o que <\/b><\/span><\/span><\/span>ocorre quando, no mesmo instante, uma crista e um vale est\u00e3o se superpondo.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

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

2<\/b><\/span><\/span><\/span>a<\/b><\/span><\/span><\/sup><\/span>\u00a0\"\" O <\/b><\/span><\/span><\/span>ponto P fica em refor\u00e7o <\/b><\/span><\/span><\/span>(interfer\u00eancia construtiva), o que <\/b><\/span><\/span><\/span>ocorre quando, no mesmo instante, duas cristas ou dois vales est\u00e3o se superpondo.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

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

II<\/b><\/span><\/span><\/span> \"\" Meio bi e tridimensional<\/b><\/span><\/span><\/span><\/p>\n

\"\"Considere a <\/b><\/span><\/span><\/span>figura<\/b><\/span><\/span><\/span> <\/b>abaixo<\/b><\/span><\/span><\/span> onde as <\/b><\/span><\/span><\/span>fontes F<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>\u00a0e F<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span>\u00a0est\u00e3o interferindo.<\/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

\"\" Procure entender e memorizar as informa\u00e7\u00f5es e rela\u00e7\u00f5es acima para <\/b><\/span><\/span><\/span>ondas sofrendo interfer\u00eancia em meios uni, bi ou tridimensionais. <\/b><\/span><\/span><\/span><\/p>\n

\"\" A <\/b><\/span><\/span><\/span>interfer\u00eancia entre duas ondas n\u00e3o atrapalha a propaga\u00e7\u00e3o de ambas<\/b><\/span><\/span><\/span> pois, a <\/b><\/span><\/span><\/span>interfer\u00eancia <\/b><\/span><\/span><\/span>\u00e9 um fen\u00f4meno que descreve a <\/b><\/span><\/span><\/span>soma das amplitudes das onda e, ap\u00f3s a mesma, elas continuam seu movimento como se nada tivesse acontecido.<\/b><\/span><\/span><\/span>\"\"<\/p>\n

E tamb\u00e9m,<\/b><\/span><\/span><\/span> <\/b>na <\/b><\/span><\/span><\/span>interfer\u00eancia entre duas ondas n\u00e3o ocorre perda de energia <\/b><\/span><\/span><\/span>pois, a <\/b><\/span><\/span><\/span>energia de uma onda est\u00e1 relacionada \u00e0 pot\u00eancia do gerador que a fez oscilar.<\/b><\/span><\/span><\/span><\/p>\n

\"\" Alguns exerc\u00edcios resolvidos, interessantes, que podem ajud\u00e1-lo a se aprofundar no assunto e melhorar seu desempenho:<\/span><\/span><\/span><\/p>\n

01-(UFC)<\/b><\/span><\/span><\/span> Duas ondas <\/b><\/span><\/span><\/span>ocupam a <\/b><\/span><\/span><\/span>mesma regi\u00e3o no espa\u00e7o <\/b><\/span><\/span><\/span>e t\u00eam <\/b><\/span><\/span><\/span>amplitudes que variam com o tempo, conforme o gr\u00e1fico a seguir.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Assinale a <\/b><\/span><\/span><\/span>alternativa <\/b><\/span><\/span><\/span>que <\/b><\/span><\/span><\/span>cont\u00e9m o gr\u00e1fico resultante <\/b><\/span><\/span><\/span>da <\/b><\/span><\/span><\/span>soma dessas duas ondas.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

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

Observe <\/b><\/span><\/span><\/span>atentamente <\/b><\/span><\/span><\/span>as <\/b><\/span><\/span><\/span>figuras<\/b><\/span><\/span><\/span> e as <\/b><\/span><\/span><\/span>explica\u00e7\u00f5es<\/b><\/span><\/span><\/span> abaixo:<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

R- C<\/b><\/span><\/span><\/span><\/p>\n

\u00a0<\/span>02-(FUVEST-SP)<\/b><\/span><\/span><\/span> <\/b>A <\/b><\/span><\/span><\/span>figura <\/b><\/span><\/span><\/span>representa, no <\/b><\/span><\/span><\/span>instante t = 0 s<\/b><\/span><\/span><\/span>, a <\/b><\/span><\/span><\/span>forma<\/b><\/span><\/span><\/span> de uma <\/b><\/span><\/span><\/span>corda esticada e presa <\/b><\/span><\/span><\/span>entre duas <\/b><\/span><\/span><\/span>paredes fixas, <\/b><\/span><\/span><\/span>na qual <\/b><\/span><\/span><\/span>dois pulsos (I e II) se propagam, sem mudar de forma, <\/b><\/span><\/span><\/span>com <\/b><\/span><\/span><\/span>velocidade de m\u00f3dulo V = 4 m\/s nos sentidos indicados. <\/b><\/span><\/span><\/span><\/p>\n

N\u00e3o h\u00e1 dissipa\u00e7\u00e3o de energia na corda. <\/b><\/span><\/span><\/span>Considere <\/b><\/span><\/span><\/span>4 pontos da corda definidos <\/b><\/span><\/span><\/span>por suas <\/b><\/span><\/span><\/span>coordenadas X:<\/b><\/span><\/span><\/span> <\/b>A<\/b><\/span><\/span><\/span> <\/b>(X<\/b><\/span><\/span><\/span>A <\/b><\/span><\/span><\/sub><\/span>= 7,0 m), B<\/b><\/span><\/span><\/span> <\/b>(X<\/b><\/span><\/span><\/span>B <\/b><\/span><\/span><\/sub><\/span>= 9,0 m,<\/b><\/span><\/span><\/span> C<\/b><\/span><\/span><\/span> (X<\/b><\/span><\/span><\/span>C <\/b><\/span><\/span><\/sub><\/span>= 11,0 m) <\/b><\/span><\/span><\/span>e <\/b><\/span><\/span><\/span>D<\/b><\/span><\/span><\/span> <\/b>(X<\/b><\/span><\/span><\/span>D <\/b><\/span><\/span><\/sub><\/span>= 13,0 m).<\/b><\/span><\/span><\/span><\/p>\n

a)<\/b><\/span><\/span><\/span> <\/b>Indique<\/b><\/span><\/span><\/span> na <\/b><\/span><\/span><\/span>figura dada<\/b><\/span><\/span><\/span>, por meio de <\/b><\/span><\/span><\/span>setas verticais,<\/b><\/span><\/span><\/span> os <\/b><\/span><\/span><\/span>sentidos <\/b><\/span><\/span><\/span>das <\/b><\/span><\/span><\/span>velocidades<\/b><\/span><\/span><\/span> na <\/b><\/span><\/span><\/span>dire\u00e7\u00e3o<\/b><\/span><\/span><\/span> do <\/b><\/span><\/span><\/span>eixo Y, <\/b><\/span><\/span><\/span>dos <\/b><\/span><\/span><\/span>pontos A e B, <\/b><\/span><\/span><\/span>no <\/b><\/span><\/span><\/span>instante t = 0 s. <\/b><\/span><\/span><\/span>Se alguma <\/b><\/span><\/span><\/span>dessas velocidades for nula, escreva \u201cnula\u201d, identificando-a.<\/b><\/span><\/span><\/span>\"\"<\/p>\n

b)<\/b><\/span><\/span><\/span> <\/b>Determine o <\/b><\/span><\/span><\/span>valor do m\u00f3dulo <\/b><\/span><\/span><\/span>da <\/b><\/span><\/span><\/span>velocidade na dire\u00e7\u00e3o do eixo Y, do ponto A, no instante t = 0 s.<\/b><\/span><\/span><\/span><\/p>\n

c)<\/b><\/span><\/span><\/span> Desenhe a forma da corda <\/b><\/span><\/span><\/span>no <\/b><\/span><\/span><\/span>instante t = 1s.<\/b><\/span><\/span><\/span> <\/b><\/p>\n

Indique por meio de setas, os sentidos das velocidades <\/b><\/span><\/span><\/span>na <\/b><\/span><\/span><\/span>dire\u00e7\u00e3o do eixo Y<\/b><\/span><\/span><\/span>, dos <\/b><\/span><\/span><\/span>pontos C e D.<\/b><\/span><\/span><\/span><\/p>\n

Se <\/b><\/span><\/span><\/span>alguma dessas velocidades for nula, <\/b><\/span><\/span><\/span>escreva <\/b><\/span><\/span><\/span>\u201cnula\u201d, identificando-a.<\/b><\/span><\/span><\/span><\/p>\n

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

a)<\/b><\/span><\/span><\/span> Os <\/b><\/span><\/span><\/span>pontos A (7m) e B (9m) <\/b><\/span><\/span><\/span>est\u00e3o no <\/b><\/span><\/span><\/span>pulso I que se move para a direita <\/b><\/span><\/span><\/span>e <\/b><\/span><\/span><\/span>localizados <\/b><\/span><\/span><\/span>conforme a <\/b><\/span><\/span><\/span><\/p>\n

\"\"figura <\/b><\/span><\/span><\/span>e suas <\/b><\/span><\/span><\/span>velocidades verticais indicadas na mesma, <\/b><\/span><\/span><\/span>redesenhando<\/b><\/span><\/span><\/span> o pulso um <\/b><\/span><\/span><\/span>pouco para a direita,<\/b><\/span><\/span><\/span> num instante imediatamente posterior t <\/b><\/span><\/span><\/span>(linha pontilhada).<\/b><\/span><\/span><\/span><\/p>\n

b) <\/b><\/span><\/span><\/span>Observe na figura <\/b><\/span><\/span><\/span>que cada deslocamento horizontal de 2 m corresponde a um deslocamento vertical de 3 cm. <\/b><\/span><\/span><\/span><\/p>\n

Assim, <\/b><\/span><\/span><\/span>enquanto <\/b><\/span><\/span><\/span>os pontos <\/b><\/span><\/span><\/span>do <\/b><\/span><\/span><\/span>pulso I se deslocam de 2m na dire\u00e7\u00e3o X com velocidade de 4 m\/s, eles<\/b><\/span><\/span><\/span> se <\/b><\/span><\/span><\/span>deslocam-se de 3 cm na dire\u00e7\u00e3o Y, <\/b><\/span><\/span><\/span>no <\/b><\/span><\/span><\/span>mesmo intervalo de tempo\u00a0\u0394t.\u00a0\u00a0\u00a0<\/b><\/span><\/span><\/span><\/p>\n

Pulso I\u00a0 \"\"<\/b><\/span><\/span><\/span>\u00a0 <\/b><\/span><\/span><\/span>V<\/b><\/span><\/span><\/span>I <\/b><\/span><\/span><\/sub><\/span>= <\/b><\/span><\/span><\/span>\u0394<\/b><\/span><\/span><\/span><\/span>X\/<\/b><\/span><\/span><\/span>\u0394<\/b><\/span><\/span><\/span><\/span>t\u00a0<\/b><\/span><\/span><\/span> \"\"\u00a0\u00a0<\/b><\/span><\/span><\/span>\u0394<\/b><\/span><\/span><\/span><\/span>t = <\/b><\/span><\/span><\/span>\u0394<\/b><\/span><\/span><\/span><\/span>X\/V<\/b><\/span><\/span><\/span>I<\/b><\/span><\/span><\/sub><\/span>\u00a0 \"\"\u00a0\u00a0<\/b><\/span><\/span><\/span>\u0394<\/b><\/span><\/span><\/span><\/span>t = 2\/4\u00a0 \"\"\u00a0<\/b><\/span><\/span><\/span>\u0394<\/b><\/span><\/span><\/span><\/span>t = 0,5 s.<\/b><\/span><\/span><\/span><\/p>\n

Nesse <\/b><\/span><\/span><\/span>mesmo intervalo de tempo\u00a0\u0394t = 0.5s, <\/b><\/span><\/span><\/span>o <\/b><\/span><\/span><\/span>ponto A,<\/b><\/span><\/span><\/span> com <\/b><\/span><\/span><\/span>velocidade V<\/b><\/span><\/span><\/span>A<\/b><\/span><\/span><\/sub><\/span>, percorreu \u0394Y= 3 cm = 0,03 m <\/b><\/span><\/span><\/span>na <\/b><\/span><\/span><\/span>dire\u00e7\u00e3o vertical\u00a0 \"\" <\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>V<\/b><\/span><\/span><\/span>A<\/b><\/span><\/span><\/sub><\/span>=\u0394Y\/\u0394t<\/b><\/span><\/span><\/span>\u00a0 \"\"\u00a0 V<\/b><\/span><\/span><\/span>A <\/b><\/span><\/span><\/sub><\/span>= 0,03\/0,5\u00a0 \"\"\u00a0\u00a0<\/b><\/span><\/span><\/span>V<\/b><\/span><\/span><\/span>A <\/b><\/span><\/span><\/sub><\/span>= 0,06 m\/s ou 6 cm\/s.\u00a0<\/b><\/span><\/span><\/span><\/p>\n

c)<\/b><\/span><\/span><\/span> <\/b>Tanto <\/b><\/span><\/span><\/span>o pulso I como o II, <\/b><\/span><\/span><\/span>com <\/b><\/span><\/span><\/span>velocidade de 4m\/s, em 1s, deslocam-se, na dire\u00e7\u00e3o X de \"\" V =<\/b><\/span><\/span><\/span><\/p>\n

\u0394<\/b><\/span><\/span><\/span><\/span>X\/<\/b><\/span><\/span><\/span>\u0394<\/b><\/span><\/span><\/span><\/span>t\u00a0 \"\"<\/b><\/span><\/span><\/span>\u00a0 4 = <\/b><\/span><\/span><\/span>\u0394<\/b><\/span><\/span><\/span><\/span>X\/1\u00a0 \"\"\u00a0\u00a0<\/b><\/span><\/span><\/span>\u0394<\/b><\/span><\/span><\/span><\/span>X = 4m.<\/b><\/span><\/span><\/span><\/p>\n

Como <\/b><\/span><\/span><\/span>cada pulso desloca-se 4m em sentidos contr\u00e1rios, <\/b><\/span><\/span><\/span>no <\/b><\/span><\/span><\/span>instante t = 1 s <\/b><\/span><\/span><\/span>eles <\/b><\/span><\/span><\/span>estar\u00e3o exatamente superpostos e ocorrer\u00e1 interfer\u00eancia destrutiva,<\/b><\/span><\/span><\/span> com a <\/b><\/span><\/span><\/span>corda exatamente na horizontal e com todos seus pontos tendo velocidade nula, inclusive C e D.<\/b><\/span><\/span><\/span>\"\"<\/p>\n

03-(UNESP-SP)<\/b><\/span><\/span><\/span> Duas fontes, F<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>\u00a0e F<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span>, est\u00e3o <\/b><\/span><\/span><\/span>emitindo sons de mesma freq\u00fc\u00eancia. <\/b><\/span><\/span><\/span><\/p>\n

Elas <\/b><\/span><\/span><\/span>est\u00e3o <\/b><\/span><\/span><\/span>posicionadas conforme ilustrado na figura<\/b><\/span><\/span><\/span>, onde se <\/b><\/span><\/span><\/span>apresenta um reticulado cuja unidade de comprimento \u00e9 dada por u = 6,0 m.<\/b><\/span><\/span><\/span>\"\"<\/p>\n

No <\/b><\/span><\/span><\/span>ponto P <\/b><\/span><\/span><\/span>ocorre <\/b><\/span><\/span><\/span>interfer\u00eancia construtiva<\/b><\/span><\/span><\/span> <\/b>entre as ondas <\/b><\/span><\/span><\/span>e \u00e9 um <\/b><\/span><\/span><\/span>ponto onde ocorre um m\u00e1ximo de intensidade.<\/b><\/span><\/span><\/span> <\/b><\/p>\n

Considerando que a <\/b><\/span><\/span><\/span>velocidade do som no ar \u00e9 340 m\/<\/b><\/span><\/span><\/span>s e que as <\/b><\/span><\/span><\/span>ondas s\u00e3o emitidas sempre em fase pelas fontes F<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>\u00a0e F<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span>\u00a0, calcule<\/b><\/span><\/span><\/span><\/p>\n

a)<\/b><\/span><\/span><\/span> <\/b>o <\/b><\/span><\/span><\/span>maior comprimento de onda<\/b><\/span><\/span><\/span> dentre os que <\/b><\/span><\/span><\/span>interferem construtivamente em P.<\/b><\/span><\/span><\/span><\/p>\n

b)<\/b><\/span><\/span><\/span> <\/b>as <\/b><\/span><\/span><\/span>duas menores freq\u00fc\u00eancias <\/b><\/span><\/span><\/span>para as quais <\/b><\/span><\/span><\/span>ocorre interfer\u00eancia construtiva em P.<\/b><\/span><\/span><\/span><\/p>\n

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

\"\"<\/p>\n

d<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span> = 6×6 = 36 m \"\" <\/b><\/span><\/span><\/span>c\u00e1lculo de <\/b><\/span><\/span><\/span>d<\/b><\/span><\/span><\/span>2 <\/b><\/span><\/span><\/sub><\/span>aplicando<\/b><\/span><\/span><\/span> pit\u00e1goras no tri\u00e2ngulo hachurado \"\" d<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span>2<\/b><\/span><\/span><\/sup><\/span> = 24<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span> + 18<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span> <\/b>= 576<\/b><\/span><\/span><\/span><\/p>\n

+ 324 = 900 \"\"<\/b><\/span><\/span><\/span> d<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span> = 30 m. <\/b><\/span><\/span><\/span><\/p>\n

a)<\/b><\/span><\/span><\/span> <\/b>Observe, na <\/b><\/span><\/span><\/span>express\u00e3o da interfer\u00eancia construtiva<\/b><\/span><\/span><\/span> da onda, onde, <\/b><\/span><\/span><\/span>d<\/b><\/span><\/span><\/span>1\u00ad<\/b><\/span><\/span><\/sub><\/span>\u00a0\u2013 d<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span>\u00a0= 2n.\u03bb\/2 \u00a0\"\"<\/b><\/span><\/span><\/span>\u00a0 <\/b><\/span><\/span><\/span>\u03bb = (d<\/b><\/span><\/span><\/span>1 <\/b><\/span><\/span><\/sub><\/span>-d<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span>)\/n\u00a0 \"\"<\/b><\/span><\/span><\/span>\u00a0 que\u00a0<\/b><\/span><\/span><\/span>\u03bb<\/b><\/span><\/span><\/span>\u00a0 e <\/b><\/span><\/span><\/span>n<\/b><\/span><\/span><\/span> s\u00e3o <\/b><\/span><\/span><\/span>inversamente proporcionais. <\/b><\/span><\/span><\/span>Assim, o <\/b><\/span><\/span><\/span>maior comprimento de onda \u03bb ocorre quando n = 1 \"\" d<\/b><\/span><\/span><\/span>1\u00ad<\/b><\/span><\/span><\/sub><\/span>\u00a0\u2013 d<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span>\u00a0= 2n.\u03bb\/2\u00a0 \"\"<\/b><\/span><\/span><\/span>\u00a0 36 – 30=2.1.\u03bb\/2\u00a0 \"\" <\/b><\/span><\/span><\/span>\u03bb = 6 m.\u00a0<\/b><\/span><\/span><\/span><\/p>\n

b)<\/b><\/span><\/span><\/span> Verifique na express\u00e3o V=\u03bbf <\/b><\/span><\/span><\/span>que, como a velociade V de propaga\u00e7\u00e3o da onda <\/b><\/span><\/span><\/span>\u00e9 constante <\/b><\/span><\/span><\/span>(mesmo meio)<\/b><\/span><\/span><\/span>,<\/b><\/span><\/span><\/span> a <\/b><\/span><\/span><\/span>freq\u00fc\u00eancia (f) e o comprimento de onda (\u03bb) s\u00e3o inversamente proporcionais.<\/b><\/span><\/span><\/span> Assim:<\/b><\/span><\/span><\/span><\/p>\n

1<\/b><\/span><\/span><\/span>a<\/b><\/span><\/span><\/sup><\/span>\u00a0menor freq\u00fc\u00eancia\u00a0 \"\"<\/b><\/span><\/span><\/span>\u00a0 <\/b><\/span><\/span><\/span>V = \u03bbf\u00a0 \"\" <\/b><\/span><\/span><\/span>340 = 6f\u00a0 \"\"\u00a0\u00a0<\/b><\/span><\/span><\/span>f = 56,7Hz.<\/b><\/span><\/span><\/span><\/p>\n

2<\/b><\/span><\/span><\/span>a<\/b><\/span><\/span><\/sup><\/span>\u00a0menor freq\u00fc\u00eancia<\/b><\/span><\/span><\/span>\u00a0 \"\"\u00a0 <\/b><\/span><\/span><\/span>d<\/b><\/span><\/span><\/span>1 <\/b><\/span><\/span><\/sub><\/span>– d<\/b><\/span><\/span><\/span>2 <\/b><\/span><\/span><\/sub><\/span>= 2n.(\u03bb\/2)\u00a0 \"\"<\/b><\/span><\/span><\/span>\u00a0 36 \u2013 30 = 2.2.\u00a0(\u03bb\/2)\u00a0 \"\"\u00a0\u00a0<\/b><\/span><\/span><\/span>\u03bb = 3m<\/b><\/span><\/span><\/span>\u00a0\u00a0\"\"\u00a0\u00a0<\/b><\/span><\/span><\/span>V = \u03bbf\u00a0 \"\"<\/b><\/span><\/span><\/span>\u00a0 340 = 3f\u00a0 \"\"\u00a0\u00a0<\/b><\/span><\/span><\/span>f = 113,3 Hz.<\/b><\/span><\/span><\/span><\/p>\n

\"\" Se voc\u00ea deseja <\/b><\/span><\/span><\/span>se aprofundar <\/b><\/span><\/span><\/span>ainda mais no assunto, selecionei <\/b><\/span><\/span><\/span>alguns exerc\u00edcios cujas resolu\u00e7\u00f5es seria interessante voc\u00ea conferir<\/b><\/span><\/span><\/span>. S\u00e3o as de <\/b><\/span><\/span><\/span>n\u00fameros 02, 06, 07, 10, 12, 14, 17, 20 e 24.<\/b><\/span><\/span><\/span><\/p>\n

 <\/p>\n

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

Interfer\u00eancia de Ondas Interfer\u00eancia de ondas em meios unidimensionais Considere dois pulsos propagando-se numa mesma corda em sentidos opostos. Ao se encontrarem ocorre a interfer\u00eancia e no encontro ocorre o fen\u00f4meno da superposi\u00e7\u00e3o e nele, cada ponto da corda corresponde \u00e0 soma das perturba\u00e7\u00f5es que seriam causadas por cada onda separadamente. Ap\u00f3s a interfer\u00eancia (cruzamento), cada pulso continua seu caminho<\/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-2419","page","type-page","status-publish","hentry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/2419","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=2419"}],"version-history":[{"count":2,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/2419\/revisions"}],"predecessor-version":[{"id":2427,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/2419\/revisions\/2427"}],"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=2419"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}