{"id":2356,"date":"2016-08-01T23:46:52","date_gmt":"2016-08-01T23:46:52","guid":{"rendered":"http:\/\/fisicaevestibular.com.br\/novo\/?page_id=2356"},"modified":"2024-08-23T14:46:38","modified_gmt":"2024-08-23T14:46:38","slug":"efeito-doppler","status":"publish","type":"page","link":"https:\/\/fisicaevestibular.com.br\/novo\/ondulatoria\/acustica\/efeito-doppler\/","title":{"rendered":"Efeito Doppler"},"content":{"rendered":"

Efeito Doppler<\/b><\/span><\/span><\/span><\/p>\n

Refere-se \u00e0 <\/b><\/span><\/span><\/span>varia\u00e7\u00e3o da freq\u00fc\u00eancia notada<\/b><\/span><\/span><\/span> por um <\/b><\/span><\/span><\/span>observador<\/b><\/span><\/span><\/span> quando a <\/b><\/span><\/span><\/span>dist\u00e2ncia entre ele e uma fonte de ondas est\u00e1 aumentando ou diminuindo.<\/b><\/span><\/span><\/span><\/p>\n

Na <\/b><\/span><\/span><\/span>aproxima\u00e7\u00e3o entre fonte e observador, <\/b><\/span><\/span><\/span>o <\/b><\/span><\/span><\/span>mesmo perceber\u00e1 o som emitido pela fonte mais agudo <\/b><\/span><\/span><\/span>(maior freq\u00fc\u00eancia, recebe maior n\u00famero de frentes de onda na unidade de tempo) do que <\/b><\/span><\/span><\/span>perceberia se fonte e observador estivessem parados. <\/b><\/span><\/span><\/span><\/p>\n

Nesse caso, o <\/b><\/span><\/span><\/span>comprimento de onda aparente percebido pelo observador ser\u00e1 menor <\/b><\/span><\/span><\/span>que o <\/b><\/span><\/span><\/span>comprimento da onda emitido pela fonte (observador O<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>\u00a0das figuras abaixo).<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

No <\/b><\/span><\/span><\/span>afastamento entre fonte e observador, <\/b><\/span><\/span><\/span>o <\/b><\/span><\/span><\/span>mesmo perceber\u00e1 o som emitido pela fonte mais grave <\/b><\/span><\/span><\/span>(menor freq\u00fc\u00eancia, recebe menor n\u00famero de frentes de onda na unidade de tempo) do que <\/b><\/span><\/span><\/span>perceberia se fonte e observador estivessem parados. <\/b><\/span><\/span><\/span><\/p>\n

Nesse caso, o <\/b><\/span><\/span><\/span>comprimento de onda aparente percebido pelo observador ser\u00e1 maior que o comprimento da onda emitido pela fonte (observador O<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span>\u00a0das figuras acima).<\/b><\/span><\/span><\/span><\/p>\n

Observe que o <\/b><\/span><\/span><\/span>motorista da ambul\u00e2ncia n\u00e3o percebe nenhuma altera\u00e7\u00e3o no som emitido pela sirene, pois eles se movem juntos.<\/b><\/span><\/span><\/span><\/p>\n

Se <\/b><\/span><\/span><\/span>denominarmos de\u00a0V\u00a0a velocidade do som,<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>V<\/b><\/span><\/span><\/span>f<\/b><\/span><\/span><\/sub><\/span>\u00a0a velocidade da fonte, V<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sub><\/span>\u00a0a velocidade do observador,\u00a0f\u00a0a freq\u00fc\u00eancia real emitida pela fonte<\/b><\/span><\/span><\/span>, a <\/b><\/span><\/span><\/span>freq\u00fc\u00eancia aparente\u00a0f<\/b><\/span><\/span><\/span>a<\/b><\/span><\/span><\/sub><\/span>\u00a0percebida pelo observador <\/b><\/span><\/span><\/span>ser\u00e1 <\/b><\/span><\/span><\/span>fornecida <\/b><\/span><\/span><\/span>pela <\/b><\/span><\/span><\/span>express\u00e3o:<\/b><\/span><\/span><\/span> <\/b><\/p>\n

\"\"<\/p>\n

Regra de sinais<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Orientando a trajet\u00f3ria do observador para a fonte<\/b><\/span><\/span><\/span>, os <\/b><\/span><\/span><\/span>sinais <\/b><\/span><\/span><\/span>de <\/b><\/span><\/span><\/span>V<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sub><\/span> e V<\/b><\/span><\/span><\/span>f<\/b><\/span><\/span><\/sub><\/span> ser\u00e3o positivos a favor dessa<\/b><\/span><\/span><\/span><\/p>\n

orienta\u00e7\u00e3o e negativos contra essa orienta\u00e7\u00e3o.<\/b><\/span><\/span><\/span><\/p>\n

Analise atentamente <\/b><\/span><\/span><\/span>os exemplos das <\/b><\/span><\/span><\/span>regras de sinais <\/b><\/span><\/span><\/span>fornecidas abaixo:<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Se observador ou fonte estiverem em repouso:<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Efeito Doppler para movimentos em qualquer dire\u00e7\u00e3o<\/b><\/span><\/span><\/span><\/p>\n

Nos estudos acima <\/b><\/span><\/span><\/span>supomos<\/b><\/span><\/span><\/span> que a <\/b><\/span><\/span><\/span>fonte e o observador estavam na mesma dire\u00e7\u00e3o do movimento.<\/b><\/span><\/span><\/span><\/p>\n

Mas a <\/b><\/span><\/span><\/span>fonte <\/b><\/span><\/span><\/span>pode <\/b><\/span><\/span><\/span>se mover numa dire\u00e7\u00e3o que forma um \u00e2ngulo\u00a0\u03b8\u00a0com a dire\u00e7\u00e3o que liga a fonte ao observador, <\/b><\/span><\/span><\/span>como na figura.<\/b><\/span><\/span><\/span>\"\"<\/p>\n

Somente a <\/b><\/span><\/span><\/span>componente da velocidade na dire\u00e7\u00e3o do observador contribui para o efeito Doppler.<\/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

\"\"<\/p>\n

Regra de sinais<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Orientando a trajet\u00f3ria do observador para a fonte<\/b><\/span><\/span><\/span>, os <\/b><\/span><\/span><\/span>sinais <\/b><\/span><\/span><\/span>de <\/b><\/span><\/span><\/span>V<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sub><\/span> e V<\/b><\/span><\/span><\/span>f<\/b><\/span><\/span><\/sub><\/span> ser\u00e3o positivos a favor dessa<\/b><\/span><\/span><\/span><\/p>\n

orienta\u00e7\u00e3o e negativos contra essa orienta\u00e7\u00e3o.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Efeito Doppler para movimentos em qualquer dire\u00e7\u00e3o<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

Frequ\u00eancia de batimento \u2013 Interfer\u00eancia sonoraInterfer\u00eancia sonora<\/b><\/span><\/span><\/span><\/p>\n

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

A <\/b><\/span><\/span><\/span>frequ\u00eancia de batimento <\/b><\/span><\/span><\/span>ocorre quando <\/b><\/span><\/span><\/span>duas ou mais ondas sonoras se superp\u00f5em num mesmo ponto.<\/b><\/span><\/span><\/span><\/p>\n

Vamos supor <\/b><\/span><\/span><\/span>duas ondas sonoras de freq\u00fc\u00eancias ligeiramente diferentes<\/b><\/span><\/span><\/span>, uma de <\/b><\/span><\/span><\/span>f<\/b><\/span><\/span><\/span>A=<\/b><\/span><\/span><\/sub><\/span>100Hz<\/b><\/span><\/span><\/span> e outra de <\/b><\/span><\/span><\/span>f<\/b><\/span><\/span><\/span>B<\/b><\/span><\/span><\/sub><\/span>=110Hz.<\/b><\/span><\/span><\/span><\/p>\n

Ent\u00e3o, <\/b><\/span><\/span><\/span>voc\u00ea ouvir\u00e1 <\/b><\/span><\/span><\/span>um <\/b><\/span><\/span><\/span>som forte <\/b><\/span><\/span><\/span>(interfer\u00eancia construtiva) e <\/b><\/span><\/span><\/span>depois <\/b><\/span><\/span><\/span>um <\/b><\/span><\/span><\/span>som fraco <\/b><\/span><\/span><\/span>(interfer\u00eancia destrutiva) e assim <\/b><\/span><\/span><\/span>sucessivamente. <\/b><\/span><\/span><\/span>Este <\/b><\/span><\/span><\/span>fen\u00f4meno recebe o nome debatimento\u00a0<\/b><\/span><\/span><\/span>(figura).<\/b><\/span><\/span><\/span><\/p>\n

\u00a0Observe que a <\/b><\/span><\/span><\/span>onda resultante apresenta pontos onde a amplitude \u00e9 m\u00e1xima <\/b><\/span><\/span><\/span>(sons fortes, interfer\u00eancia construtiva) como nos pontos <\/b><\/span><\/span><\/span>A, C e E<\/b><\/span><\/span><\/span>, vai diminuindo e <\/b><\/span><\/span><\/span>praticamente desaparece ou se anula (interfer\u00eancia destrutiva) <\/b><\/span><\/span><\/span>como nos pontos <\/b><\/span><\/span><\/span>B, D e F.<\/b><\/span><\/span><\/span>\"\"<\/p>\n

A <\/b><\/span><\/span><\/span>freq\u00fc\u00eancia do batimento <\/b><\/span><\/span><\/span>\u00e9 definida como sendo <\/b><\/span><\/span><\/span>f<\/b><\/span><\/span><\/span>batimento <\/b><\/span><\/span><\/sub><\/span>= f<\/b><\/span><\/span><\/span>maior<\/b><\/span><\/span><\/sub><\/span>\u00a0\u2013 f<\/b><\/span><\/span><\/span>menor<\/b><\/span><\/span><\/sub><\/span>.<\/b><\/span><\/span><\/span> <\/b><\/p>\n

O <\/b><\/span><\/span><\/span>fen\u00f4meno do batimento <\/b><\/span><\/span><\/span>\u00e9 muitas vezes utilizado na <\/b><\/span><\/span><\/span>afina\u00e7\u00e3o de instrumentos musicais.<\/b><\/span><\/span><\/span> Se as freq\u00fc\u00eancias da fonte afiadora e do instrumento forem diferentes, ouve-se o batimento. A <\/b><\/span><\/span><\/span>freq\u00fc\u00eancia do batimento vai diminuindo \u00e0 medida que o instrumento vai sendo afinado <\/b><\/span><\/span><\/span>e, quando <\/b><\/span><\/span><\/span>desaparecer, o instrumento estar\u00e1 afinado<\/b><\/span><\/span><\/span>.<\/span><\/span><\/p>\n

Utilidades do Efeito Doppler<\/b><\/span><\/span><\/span><\/p>\n

\"\" Nos diagn\u00f3sticos m\u00e9dicos pela ultra-sonografia ou ecografia<\/b><\/span><\/span><\/span> \"\" <\/b><\/span><\/span><\/span>\u00a0<\/b><\/span>um <\/b><\/span><\/span><\/span>m\u00e9todo diagn\u00f3stico <\/b><\/span><\/span><\/span>que aproveita o <\/b><\/span><\/span><\/span>eco produzido pelo som para ver em tempo real as sombras produzidas pelas estruturas e \u00f3rg\u00e3os do organismo<\/b><\/span><\/span><\/span>. <\/b><\/span><\/span><\/span><\/p>\n

Os <\/b><\/span><\/span><\/span>aparelhos de ultra-som <\/b><\/span><\/span><\/span>em geral utilizam uma <\/b><\/span><\/span><\/span>freq\u00fc\u00eancia <\/b><\/span><\/span><\/span>pr\u00f3xima de 1 MHz, <\/b><\/span><\/span><\/span>emitidas<\/b><\/span><\/span><\/span> por uma <\/b><\/span><\/span><\/span>fonte sonora colocada contato com a pele <\/b><\/span><\/span><\/span>e <\/b><\/span><\/span><\/span>recebendo os ecos gerados, <\/b><\/span><\/span><\/span>que s\u00e3o <\/b><\/span><\/span><\/span>interpretados <\/b><\/span><\/span><\/span>atrav\u00e9s da <\/b><\/span><\/span><\/span>computa\u00e7\u00e3o gr\u00e1fica.<\/b><\/span><\/span><\/span> <\/b><\/p>\n

Dependendo da <\/b><\/span><\/span><\/span>densidade e composi\u00e7\u00e3o das estruturas internas do corpo<\/b><\/span><\/span><\/span> a <\/b><\/span><\/span><\/span>atenua\u00e7\u00e3o<\/b><\/span><\/span><\/span> e <\/b><\/span><\/span><\/span>mudan\u00e7a de fase dos sinais emitidos <\/b><\/span><\/span><\/span>varia, sendo <\/b><\/span><\/span><\/span>poss\u00edvel a tradu\u00e7\u00e3o em uma escala de cinza, que formar\u00e1 a imagem dos \u00f3rg\u00e3os internos.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Mas, existem <\/b><\/span><\/span><\/span>equipamentos de ultra-sonografia <\/b><\/span><\/span><\/span>que <\/b><\/span><\/span><\/span>alem das imagens <\/b><\/span><\/span><\/span>permitem <\/b><\/span><\/span><\/span>avaliar<\/b><\/span><\/span><\/span> as <\/b><\/span><\/span><\/span>velocidade de deslocamentos do sangue.<\/b><\/span><\/span><\/span><\/p>\n

Estes equipamentos <\/b><\/span><\/span><\/span>comparam a freq\u00fc\u00eancia do ultra-som emitido <\/b><\/span><\/span><\/span>com a <\/b><\/span><\/span><\/span>freq\u00fc\u00eancia do refletido e <\/b><\/span><\/span><\/span>atrav\u00e9s do <\/b><\/span><\/span><\/span>Efeito Doppler determinam as velocidades de deslocamento, cujo conhecimento \u00e9 um dado muito importante para os diagn\u00f3sticos m\u00e9dicos nas seguintes \u00e1reas:.<\/b><\/span><\/span><\/span><\/p>\n

\"\" Estudo de <\/b><\/span><\/span><\/span>art\u00e9rias e veias;<\/b><\/span><\/span><\/span><\/p>\n

\"\" Detec\u00e7\u00e3o de <\/b><\/span><\/span><\/span>tromboses venosas ou arteriais; <\/b><\/span><\/span><\/span><\/p>\n

\"\" Estenoses<\/b><\/span><\/span><\/span> e ou <\/b><\/span><\/span><\/span>oclus\u00f5es arteriais; <\/b><\/span><\/span><\/span><\/p>\n

\"\" Aneurismas; <\/b><\/span><\/span><\/span><\/p>\n

\"\" Mapeamento <\/b><\/span><\/span><\/span>pr\u00e9-operat\u00f3rio de varizes;<\/b><\/span><\/span><\/span><\/p>\n

\"\" Gravidez <\/b><\/span><\/span><\/span>para a aferi\u00e7\u00e3o do <\/b><\/span><\/span><\/span>fluxo sangu\u00edneo materno-fetal; <\/b><\/span><\/span><\/span><\/p>\n

\"\" Doen\u00e7as das art\u00e9rias renais <\/b><\/span><\/span><\/span>(estreitamentos, obstru\u00e7\u00f5es e dilata\u00e7\u00f5es).<\/b><\/span><\/span><\/span><\/p>\n

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

\"\" O <\/b><\/span><\/span><\/span>funcionamento do radar do tipo Doppler <\/b><\/span><\/span><\/span>baseia-se nos <\/b><\/span><\/span><\/span>deslocamentos dos m\u00f3veis. <\/b><\/span><\/span><\/span>O aparelho <\/b><\/span><\/span><\/span>emite<\/b><\/span><\/span><\/span> uma <\/b><\/span><\/span><\/span>onda eletromagn\u00e9tica de freq\u00fc\u00eancia (f\u2019) cont\u00ednua e constante.<\/b><\/span><\/span><\/span> <\/b><\/p>\n

Se o <\/b><\/span><\/span><\/span>corpo em movimento,<\/b><\/span><\/span><\/span> (por exemplo, autom\u00f3vel) em quest\u00e3o estiver se <\/b><\/span><\/span><\/span>movimentando em dire\u00e7\u00e3o \u00e0 fonte, o receptor do radar identificar\u00e1 um aumento na freq\u00fcencia (f\u2019\u2019).<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

A <\/b><\/span><\/span><\/span>diferen\u00e7a entre as freq\u00fcencias emitidas (f\u2019) e refletidas (f\u2019\u2019) <\/b><\/span><\/span><\/span>ser\u00e1 <\/b><\/span><\/span><\/span>traduzida pelo decodificador <\/b><\/span><\/span><\/span>no radar como um <\/b><\/span><\/span><\/span>valor de velocidade.<\/b><\/span><\/span><\/span> <\/b><\/p>\n

Esse <\/b><\/span><\/span><\/span>tipo de radar <\/b><\/span><\/span><\/span>tamb\u00e9m funciona quando o <\/b><\/span><\/span><\/span>m\u00f3vel est\u00e1 se afastando. <\/b><\/span><\/span><\/span><\/p>\n

Novamente o que est\u00e1 em jogo \u00e9 a <\/b><\/span><\/span><\/span>diferen\u00e7a entre as freq\u00fcencias de emiss\u00e3o e de recep\u00e7\u00e3o<\/b><\/span><\/span><\/span>, que permitem avaliar a <\/b><\/span><\/span><\/span>velocidade da superf\u00edcie refletora.<\/b><\/span><\/span><\/span><\/p>\n

O\u00a0<\/b><\/span><\/span><\/span>controle de tr\u00e1fego a\u00e9reo<\/b><\/span><\/span><\/span><\/a>\u00a0usa radares para rastrear\u00a0<\/b><\/span><\/span><\/span>avi\u00f5es<\/b><\/span><\/span><\/span><\/a>\u00a0no solo como no ar, al\u00e9m de us\u00e1-lo tamb\u00e9m na hora de <\/b><\/span><\/span><\/span>orientar os pilotos para que fa\u00e7am pousos suaves. <\/b><\/span><\/span><\/span><\/p>\n

J\u00e1 <\/b><\/span><\/span><\/span>a Nasa os usa para mapear a Terra e outros planetas, <\/b><\/span><\/span><\/span>para <\/b><\/span><\/span><\/span>rastrear\u00a0<\/b><\/span><\/span><\/span>sat\u00e9lites<\/b><\/span><\/span><\/span><\/a>\u00a0e fragmentos espaciais e para ajudar na hora de manobrar suas aeronaves.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Os <\/b><\/span><\/span><\/span>meteorologistas<\/b><\/span><\/span><\/span> usam radares para <\/b><\/span><\/span><\/span>rastrear tempestades,\u00a0<\/b><\/span><\/span><\/span>furac\u00f5es<\/b><\/span><\/span><\/span><\/a>\u00a0e\u00a0<\/b><\/span><\/span><\/span>tornados<\/b><\/span><\/span><\/span><\/a>. <\/b><\/span><\/span><\/span><\/p>\n

At\u00e9 o <\/b><\/span><\/span><\/span>dispositivo que faz as portas das lojas abrirem automaticamente \u00e9 um tipo de radar. <\/b><\/span><\/span><\/span><\/p>\n

\"\" O <\/b><\/span><\/span><\/span>efeito Doppler <\/b><\/span><\/span><\/span>tamb\u00e9m \u00e9 <\/b><\/span><\/span><\/span>v\u00e1lido para a luz <\/b><\/span><\/span><\/span>(onda eletromagn\u00e9tica transversal).<\/b><\/span><\/span><\/span><\/p>\n

Assim, a <\/b><\/span><\/span><\/span>frequ\u00eancia da luz aumenta <\/b><\/span><\/span><\/span>( a <\/b><\/span><\/span><\/span>cor da luz <\/b><\/span><\/span><\/span>tende para o <\/b><\/span><\/span><\/span>azul<\/b><\/span><\/span><\/span>) quando a <\/b><\/span><\/span><\/span>dist\u00e2ncia observador- fonte estiver diminuindo <\/b><\/span><\/span><\/span>e <\/b><\/span><\/span><\/span>diminui<\/b><\/span><\/span><\/span> (a <\/b><\/span><\/span><\/span>cor da luz <\/b><\/span><\/span><\/span>tende para o <\/b><\/span><\/span><\/span>vermelho<\/b><\/span><\/span><\/span>) quando a <\/b><\/span><\/span><\/span>dist\u00e2ncia observador-fonte estiver aumentando<\/b><\/span><\/span><\/span>. A <\/b><\/span><\/span><\/span>velocidade relativa observador-fonte \u00e9 muito grande.<\/b><\/span><\/span><\/span><\/p>\n

Assim, devido ao <\/b><\/span><\/span><\/span>efeito Doppler, as cores do espectro eletromagn\u00e9tico de uma estrela aparecem<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

deslocadas para o vermelho, caso o astro observado esteja se afastando<\/b><\/span><\/span><\/span>, ou <\/b><\/span><\/span><\/span>deslocadas para o azul, no caso do astro estar se aproximando de n\u00f3s.<\/b><\/span><\/span><\/span><\/p>\n

Na astronomia, o <\/b><\/span><\/span><\/span>efeito Doppler \u00e9 utilizado <\/b><\/span><\/span><\/span>para medir a <\/b><\/span><\/span><\/span>velocidade relativa das estrelas <\/b><\/span><\/span><\/span>e outros corpos celestes luminosos em <\/b><\/span><\/span><\/span>rela\u00e7\u00e3o \u00e0 Terra.<\/b><\/span><\/span><\/span><\/p>\n

Essas medidas <\/b><\/span><\/span><\/span>fizeram os cientistas conclu\u00edrem que o <\/b><\/span><\/span><\/span>universo est\u00e1 em expans\u00e3o, pois a cor destes corpos celestes luminosos apresenta maior desvio para o vermelho o que indica que a dist\u00e2ncia entre eles e n\u00f3s est\u00e1 aumentando.<\/b><\/span><\/span><\/span><\/p>\n

\"\" Se voc\u00ear quizer, pode <\/b><\/span><\/span><\/span>conferir as resolu\u00e7\u00f5es <\/b><\/span><\/span><\/span>de alguns exerc\u00edcios que <\/b><\/span><\/span><\/span>podem ser \u00fateis<\/b><\/span><\/span><\/span> e que selecionei \"\" <\/b><\/span><\/span><\/span>s\u00e3o<\/b><\/span><\/span><\/span> os de <\/b><\/span><\/span><\/span>n\u00fameros, 04, 09, 11, 16, 17, 19 e 29.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Veja a resolu\u00e7\u00e3o de alguns exerc\u00edcios interessantes:<\/b><\/span><\/span><\/span><\/p>\n

01-(FUVEST-SP)<\/b><\/span><\/span><\/span> Uma <\/b><\/span><\/span><\/span>onda sonora <\/b><\/span><\/span><\/span>considerada plana, <\/b><\/span><\/span><\/span>proveniente de uma sirene em repouso, <\/b><\/span><\/span><\/span>propaga-se no <\/b><\/span><\/span><\/span>ar parado, na dire\u00e7\u00e3o horizontal, <\/b><\/span><\/span><\/span>com <\/b><\/span><\/span><\/span>velocidade V igual a 330m\/s e comprimento de onda igual a 16,5cm.<\/b><\/span><\/span><\/span>\"\"<\/p>\n

Na <\/b><\/span><\/span><\/span>regi\u00e3o em que a onda est\u00e1 se propagando,<\/b><\/span><\/span><\/span> um <\/b><\/span><\/span><\/span>atleta corre, <\/b><\/span><\/span><\/span>em uma <\/b><\/span><\/span><\/span>pista horizontal,<\/b><\/span><\/span><\/span> com <\/b><\/span><\/span><\/span>velocidade U igual a 6,60m\/s, <\/b><\/span><\/span><\/span>formando um <\/b><\/span><\/span><\/span>\u00e2ngulo de 60\u00b0 com a dire\u00e7\u00e3o de propaga\u00e7\u00e3o da onda<\/b><\/span><\/span><\/span>. <\/b><\/span><\/span><\/span><\/p>\n

Determine <\/b><\/span><\/span><\/span>a <\/b><\/span><\/span><\/span>frequ\u00eancia aproximada <\/b><\/span><\/span><\/span>do <\/b><\/span><\/span><\/span>som ouvido pelo atleta.<\/b><\/span><\/span><\/span><\/p>\n

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

A <\/b><\/span><\/span><\/span>velocidade de propaga\u00e7\u00e3o das ondas V e a velocidade do observador (receptor) U<\/b><\/span><\/span><\/span> devem estar na <\/b><\/span><\/span><\/span>mesma dire\u00e7\u00e3o.<\/b><\/span><\/span><\/span><\/p>\n

Apenas a <\/b><\/span><\/span><\/span>componente horizontal (U<\/b><\/span><\/span><\/span>x<\/b><\/span><\/span><\/sub><\/span>) da velocidade (U) <\/b><\/span><\/span><\/span>do observador\u00a0<\/b><\/span><\/span><\/span>influi no movimento<\/b><\/span><\/span><\/span>, pois as frentes de onda s\u00e3o planas, se <\/b><\/span><\/span><\/span>propagando na horizontal e para a direita. Veja que a componente vertical de U n\u00e3o atinge o observador <\/b><\/span><\/span><\/span>e voc\u00ea <\/b><\/span><\/span><\/span>deve considerar apenas a componente sobre a reta que liga o observador \u00e0 fonte:<\/b><\/span><\/span><\/span> (vide figuras).<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Projetando U na dire\u00e7\u00e3o de V \"\"<\/b><\/span><\/span><\/span> <\/b>U<\/b><\/span><\/span><\/span>x <\/b><\/span><\/span><\/sub><\/span>= Ucos60<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sup><\/span>\u00a0 \"\"<\/b><\/span><\/span><\/span>\u00a0 U<\/b><\/span><\/span><\/span>x <\/b><\/span><\/span><\/sub><\/span>= 6,6.0,5\u00a0 \"\"\u00a0 <\/b><\/span><\/span><\/span>U<\/b><\/span><\/span><\/span>x <\/b><\/span><\/span><\/sub><\/span>= 3,3m\/s.<\/b><\/span><\/span><\/span>\u00a0\u00a0 <\/b><\/span><\/span><\/span><\/p>\n

C\u00e1lculo da <\/b><\/span><\/span><\/span>freq\u00fc\u00eancia da fonte <\/b><\/span><\/span><\/span>pela <\/b><\/span><\/span><\/span>equa\u00e7\u00e3o fundamental da ondulat\u00f3ria\u00a0 \"\"<\/b><\/span><\/span><\/span>\u00a0V = \u03bbf\u00a0 \"\"\u00a0 330 = 0,165f\u00a0 \"\"\u00a0 <\/b><\/span><\/span><\/span>f = 2.000Hz.<\/b><\/span><\/span><\/span><\/p>\n

A <\/b><\/span><\/span><\/span>velocidade da fonte \u00e9 nula<\/b><\/span><\/span><\/span>, pois a <\/b><\/span><\/span><\/span>sirene<\/b><\/span><\/span><\/span> est\u00e1 em <\/b><\/span><\/span><\/span>repouso<\/b><\/span><\/span><\/span> \"\" <\/b><\/span><\/span><\/span>V<\/b><\/span><\/span><\/span>F<\/b><\/span><\/span><\/sub><\/span> = 0<\/b><\/span><\/span><\/span><\/p>\n

C\u00e1lculo da <\/b><\/span><\/span><\/span>frequ\u00eancia aparente <\/b><\/span><\/span><\/span>percebida pelo atleta pela <\/b><\/span><\/span><\/span>express\u00e3o do efeito Doppler<\/b><\/span><\/span><\/span> \"\" <\/b><\/span><\/span><\/span>f<\/b><\/span><\/span><\/span>a<\/b><\/span><\/span><\/sub><\/span> = f.(V \u00b1 V<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sub><\/span>)\/(V \u00b1 V<\/b><\/span><\/span><\/span>F<\/b><\/span><\/span><\/sub><\/span>) \"\"<\/b><\/span><\/span><\/span> <\/b>f<\/b><\/span><\/span><\/span>a <\/b><\/span><\/span><\/sub><\/span>=2000(330-3,3)\/(330 \u2013 0)<\/b><\/span><\/span><\/span>\u00a0 \"\"\u00a0 f<\/b><\/span><\/span><\/span>a <\/b><\/span><\/span><\/sub><\/span>= 653.400\/330\u00a0 \"\"\u00a0\u00a0<\/b><\/span><\/span><\/span>f<\/b><\/span><\/span><\/span>a<\/b><\/span><\/span><\/sub><\/span> = 1.980 Hz\u00a0\u00a0 <\/b><\/span><\/span><\/span><\/p>\n

Observa\u00e7\u00e3o: Voc\u00ea obteria o mesmo resultado se projetasse V na dire\u00e7\u00e3o de U.<\/b><\/span><\/span><\/span><\/p>\n

02- (UFJF-MG)<\/b><\/span><\/span><\/span> <\/b>Um <\/b><\/span><\/span><\/span>alarme de seguran\u00e7a, <\/b><\/span><\/span><\/span>que <\/b><\/span><\/span><\/span>est\u00e1 fixo,<\/b><\/span><\/span><\/span> \u00e9 acionado, produzindo um <\/b><\/span><\/span><\/span>som com uma freq\u00fc\u00eancia de 735 Hz. <\/b><\/span><\/span><\/span><\/p>\n

Considere a <\/b><\/span><\/span><\/span>velocidade do som no ar como sendo de 343 m\/s<\/b><\/span><\/span><\/span>. Quando uma pessoa <\/b><\/span><\/span><\/span>dirige um carro <\/b><\/span><\/span><\/span>em <\/b><\/span><\/span><\/span>dire\u00e7\u00e3o ao\u00a0 alarme <\/b><\/span><\/span><\/span>e depois s<\/b><\/span><\/span><\/span>e afasta dele com a mesma velocidade, <\/b><\/span><\/span><\/span>observa uma <\/b><\/span><\/span><\/span>mudan\u00e7a na freq\u00fc\u00eancia de 78,4 Hz.<\/b><\/span><\/span><\/span><\/p>\n

a)<\/b><\/span><\/span><\/span> <\/b>A <\/b><\/span><\/span><\/span>freq\u00fc\u00eancia ouvida pela pes<\/b><\/span><\/span><\/span>soa quando ela se <\/b><\/span><\/span><\/span>aproxima da sirene, <\/b><\/span><\/span><\/span>\u00e9 <\/b><\/span><\/span><\/span>maior ou menor do que ouviria se ela estivesse parada? Justifique.<\/b><\/span><\/span><\/span><\/p>\n

b)<\/b><\/span><\/span><\/span> <\/b>Qual \u00e9 o <\/b><\/span><\/span><\/span>m\u00f3dulo da velocidade do carro?<\/b><\/span><\/span><\/span><\/p>\n

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

a)<\/b><\/span><\/span><\/span> <\/b>Maior. <\/b><\/span><\/span><\/span>\u00c0 <\/b><\/span><\/span><\/span>medida<\/b><\/span><\/span><\/span> que a pessoa se <\/b><\/span><\/span><\/span>aproxima da fonte, ele observa um aumento do n\u00famero de frentes de onda passando por ele por unidade de tempo <\/b><\/span><\/span><\/span>em rela\u00e7\u00e3o<\/b><\/span><\/span><\/span> \u00e0 situa\u00e7\u00e3o em que a pessoa se encontra parada, <\/b><\/span><\/span><\/span>implicando num <\/b><\/span><\/span><\/span>aumento da freq\u00fc\u00eancia.<\/b><\/span><\/span><\/span><\/p>\n

b)<\/b><\/span><\/span><\/span> Se aproximando\u00a0 \"\"<\/b><\/span><\/span><\/span>\u00a0 f<\/b><\/span><\/span><\/span>1 <\/b><\/span><\/span><\/sub><\/span>= 735(343+V)\/343\u00a0 \"\"\u00a0 <\/b><\/span><\/span><\/span>f<\/b><\/span><\/span><\/span>1 <\/b><\/span><\/span><\/sub><\/span>= 735 + 2,1V<\/b><\/span><\/span><\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0 <\/span>Se afastando\u00a0 \"\"<\/b><\/span><\/span><\/span>\u00a0 f<\/b><\/span><\/span><\/span>2 <\/b><\/span><\/span><\/sub><\/span>= 735(343-V)\/343\u00a0 \"\"\u00a0 <\/b><\/span><\/span><\/span>f<\/b><\/span><\/span><\/span>2 <\/b><\/span><\/span><\/sub><\/span>= 735-2,1V<\/b><\/span><\/span><\/span><\/p>\n

\u00c8 fornecida a mudan\u00e7a <\/b><\/span><\/span><\/span>(varia\u00e7\u00e3o) de <\/b><\/span><\/span><\/span>frequ\u00eancia <\/b><\/span><\/span><\/span>\u0394<\/b><\/span><\/span><\/span><\/span>f = 78 Hz \u00a0\"\"<\/b><\/span><\/span><\/span>\u00a0\u00a0\u00a0<\/b><\/span><\/span><\/span>\u0394<\/b><\/span><\/span><\/span><\/span>f = f<\/b><\/span><\/span><\/span>1 <\/b><\/span><\/span><\/sub><\/span>– f<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span>\u00a0 \"\"<\/b><\/span><\/span><\/span>\u00a0 78 = 735 + 2,1V \u2013 (735-2,1V)\u00a0 \"\"\u00a0 78 = 735+2,1V – 735 +2,1V\u00a0 \"\"\u00a0 <\/b><\/span><\/span><\/span>V = 18,6m\/s<\/b><\/span><\/span><\/span><\/p>\n

03-<\/b><\/span><\/span><\/span> <\/b>Deslocando-se \u00e0\u00a0<\/b><\/span><\/span><\/span>velocidade de 144 km\/h\u00a0por uma via,<\/b><\/span><\/span><\/span> uma\u00a0<\/b><\/span><\/span><\/span>viatura da pol\u00edcia rodovi\u00e1ria<\/b><\/span><\/span><\/span>, em persegui\u00e7\u00e3o,\u00a0<\/b><\/span><\/span><\/span>toca a sirene, cujo som tem\u00a0frequ\u00eancia igual a 1500 Hz<\/b><\/span><\/span><\/span>. <\/b><\/span><\/span><\/span><\/p>\n

Uma\u00a0<\/b><\/span><\/span><\/span>mulher parada\u00a0<\/b><\/span><\/span><\/span>num ponto<\/b><\/span><\/span><\/span>\"\"<\/p>\n

de \u00f4nibus, na mesma via, <\/b><\/span><\/span><\/span>percebe uma\u00a0varia\u00e7\u00e3o brusca no som, no instante em que a viatura passa pelo ponto onde ela se encontra. Qual \u00e9, <\/b><\/span><\/span><\/span>em valor aproximado, a\u00a0<\/b><\/span><\/span><\/span>varia\u00e7\u00e3o de frequ\u00eancia, em Hz, ouvida pela mulher,<\/b><\/span><\/span><\/span> tendo como par\u00e2metro os <\/b><\/span><\/span><\/span>per\u00edodos anterior e posterior \u00e0 passagem da viatura?<\/b><\/span><\/span><\/span><\/p>\n

Adote a <\/b><\/span><\/span><\/span>velocidade do som\u00a0V<\/b><\/span><\/span><\/span>s<\/b><\/span><\/span><\/sub><\/span>\u00a0= 340m\/s<\/b><\/span><\/span><\/span><\/p>\n

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

Fonte se\u00a0aproximando\u00a0da mulher<\/b><\/span><\/span><\/span> \"\"\u00a0<\/b><\/span><\/span><\/span>f<\/b><\/span><\/span><\/span>a <\/b><\/span><\/span><\/sub><\/span>= 1500(340 + 0)\/(340 – 40) <\/b><\/span><\/span><\/span>= 1500.340\/300 \"\"\u00a0<\/b><\/span><\/span><\/span>f<\/b><\/span><\/span><\/span>a <\/b><\/span><\/span><\/sub><\/span>= 1700Hz<\/b><\/span><\/span><\/span><\/p>\n

Fonte se\u00a0afastando\u00a0da mulher<\/b><\/span><\/span><\/span> \"\" \u00a0<\/b><\/span><\/span><\/span>f<\/b><\/span><\/span><\/span>a <\/b><\/span><\/span><\/sub><\/span>= 1500(340 + 0)\/(340 +40) <\/b><\/span><\/span><\/span>= 1500.340\/380 \"\"\u00a0<\/b><\/span><\/span><\/span>f<\/b><\/span><\/span><\/span>a <\/b><\/span><\/span><\/sub><\/span>= 1342,6Hz<\/b><\/span><\/span><\/span><\/p>\n

\u0394f <\/b><\/span><\/span><\/span>= 1700 \u2013 1342 <\/b><\/span><\/span><\/span>= 358Hz.<\/b><\/span><\/span><\/span><\/p>\n

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

03-\u00a0(ITA-SP) <\/b><\/span><\/span><\/span>Uma <\/b><\/span><\/span><\/span>jovem encontra-se no assento de um carrossel circular <\/b><\/span><\/span><\/span>que <\/b><\/span><\/span><\/span>gira a uma velocidade<\/b><\/span><\/span><\/span><\/p>\n

angular constante com per\u00edodo T. <\/b><\/span><\/span><\/span>\"\"<\/p>\n

Uma <\/b><\/span><\/span><\/span>sirene posicionada fora do carrossel <\/b><\/span><\/span><\/span>emite um <\/b><\/span><\/span><\/span>som de frequ\u00eancia f<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sub><\/span>\u00a0em dire\u00e7\u00e3o ao centro de rota\u00e7\u00e3o.<\/b><\/span><\/span><\/span><\/p>\n

No <\/b><\/span><\/span><\/span>instante t = 0, a jovem est\u00e1 a menor dist\u00e2ncia em rela\u00e7\u00e3o <\/b><\/span><\/span><\/span>\u00e0 <\/b><\/span><\/span><\/span>sirene.\u00a0<\/b><\/span><\/span><\/span><\/p>\n

Nesta situa\u00e7\u00e3o, <\/b><\/span><\/span><\/span>assinale a melhor representa\u00e7\u00e3o da frequ\u00eancia f ouvida pela jovem.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Observe\u00a0o esquema da <\/b><\/span><\/span><\/span>figura abaixo:<\/b><\/span><\/span><\/span><\/p>\n

\"\" No <\/b><\/span><\/span><\/span>instante t = 0 a jovem <\/b><\/span><\/span><\/span>(ouvinte ou observador) est\u00e1 na <\/b><\/span><\/span><\/span>posi\u00e7\u00e3o mostrada na figura\u00a0\"\"<\/b><\/span><\/span><\/span>\u00a0\u00a0nesse ponto, a <\/b><\/span><\/span><\/span>frequ\u00eancia ouvida (f<\/b><\/span><\/span><\/span>) <\/b><\/span><\/span><\/span>\u00e9 igual a frequ\u00eancia da sirene (f<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sub><\/span>) <\/b><\/span><\/span><\/span>\u201crecebe a mesma quantidade de ondas que as emitidas pela sirene, mesmo \u03bb\u201d tal que <\/b><\/span><\/span><\/span>f\/f<\/b><\/span><\/span><\/span>o <\/b><\/span><\/span><\/sub><\/span>= 1\u00a0(f = f<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sub><\/span>).<\/b><\/span><\/span><\/span>\"\"<\/p>\n

\"\" A <\/b><\/span><\/span><\/span>partir <\/b><\/span><\/span><\/span>desse instante, <\/b><\/span><\/span><\/span>at\u00e9T\/2, h\u00e1 afastamento relativo entre a jovem e a sirene,<\/b><\/span><\/span><\/span> de modo que a <\/b><\/span><\/span><\/span>frequ\u00eancia ouvida por ela \u00e9 menor que a frequ\u00eancia emitida pela sirene f\/f<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sub><\/span><1 (f < f<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sub><\/span>).<\/b><\/span><\/span><\/span><\/p>\n

\"\" no instante t =T\/2, <\/b><\/span><\/span><\/span>ela <\/b><\/span><\/span><\/span>volta a ouvir a frequ\u00eancia emitida pela fonte\u00a0<\/b><\/span><\/span><\/span>(recebe a mesma quantidade de ondas que as emitidas pela sirene, mesmo \u03bb) tal que <\/b><\/span><\/span><\/span>f\/f<\/b><\/span><\/span><\/span>o <\/b><\/span><\/span><\/sub><\/span>= 1\u00a0(f = f<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sub><\/span>).<\/b><\/span><\/span><\/span><\/p>\n

\"\" De <\/b><\/span><\/span><\/span>T\/2 at\u00e9 T, <\/b><\/span><\/span><\/span>ocorre <\/b><\/span><\/span><\/span>aproxima\u00e7\u00e3o relativa entre a jovem e a sirene e ela passa a perceber uma frequ\u00eancia maior que a emitida pela sirene f\/f<\/b><\/span><\/span><\/span>o <\/b><\/span><\/span><\/sub><\/span>> 1 (f > f<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sub><\/span>).<\/b><\/span><\/span><\/span><\/p>\n

Observe que <\/b><\/span><\/span><\/span>as velocidades m\u00e1ximas de afastamento e de aproxima\u00e7\u00e3o ocorrem em t = T\/4 e em t = 3T\/4, <\/b><\/span><\/span><\/span>instantes <\/b><\/span><\/span><\/span>em f\/f<\/b><\/span><\/span><\/span>o <\/b><\/span><\/span><\/sub><\/span>atinge <\/b><\/span><\/span><\/span>valores m\u00ednimo e m\u00e1ximo, respectivamente <\/b><\/span><\/span><\/span>\u00a0\"\"\u00a0\u00a0<\/b><\/span><\/span><\/span>R- A<\/b><\/span><\/span><\/span><\/p>\n

 <\/p>\n

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

Efeito Doppler Refere-se \u00e0 varia\u00e7\u00e3o da freq\u00fc\u00eancia notada por um observador quando a dist\u00e2ncia entre ele e uma fonte de ondas est\u00e1 aumentando ou diminuindo. Na aproxima\u00e7\u00e3o entre fonte e observador, o mesmo perceber\u00e1 o som emitido pela fonte mais agudo (maior freq\u00fc\u00eancia, recebe maior n\u00famero de frentes de onda na unidade de tempo) do que perceberia se fonte e<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":2325,"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-2356","page","type-page","status-publish","hentry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/2356","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=2356"}],"version-history":[{"count":3,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/2356\/revisions"}],"predecessor-version":[{"id":2365,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/2356\/revisions\/2365"}],"up":[{"embeddable":true,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/2325"}],"wp:attachment":[{"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/media?parent=2356"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}