{"id":2377,"date":"2016-08-02T00:17:15","date_gmt":"2016-08-02T00:17:15","guid":{"rendered":"http:\/\/fisicaevestibular.com.br\/novo\/?page_id=2377"},"modified":"2024-08-23T14:48:47","modified_gmt":"2024-08-23T14:48:47","slug":"ondas-estacionarias","status":"publish","type":"page","link":"https:\/\/fisicaevestibular.com.br\/novo\/ondulatoria\/acustica\/ondas-estacionarias\/","title":{"rendered":"Ondas Estacion\u00e1rias"},"content":{"rendered":"

Ondas Estacion\u00e1rias<\/b><\/span><\/span><\/span><\/p>\n

Forma\u00e7\u00e3o de ondas estacion\u00e1rias<\/b><\/span><\/span><\/span><\/p>\n

Obtemos\u00a0<\/b><\/span><\/span><\/span>ondas estacion\u00e1rias<\/b><\/span><\/span><\/span>\u00a0pela <\/b><\/span><\/span><\/span>superposi\u00e7\u00e3o de duas ondas id\u00eanticas,<\/b><\/span><\/span><\/span> de <\/b><\/span><\/span><\/span>mesma amplitude, mesma frequ\u00eancia, mesmo comprimento de onda<\/b><\/span><\/span><\/span> e que se <\/b><\/span><\/span><\/span>movem na mesma dire\u00e7\u00e3o e sentidos opostos.<\/b><\/span><\/span><\/span><\/p>\n

Considere uma <\/b><\/span><\/span><\/span>corda fixa em <\/b><\/span><\/span><\/span>uma da<\/b><\/span><\/span><\/span>s extremidades e <\/b><\/span><\/span><\/span>na outra<\/b><\/span><\/span><\/span> uma fonte produz ondas peri\u00f3dicas<\/b><\/span><\/span><\/span> <\/b><\/p>\n

que, ao <\/b><\/span><\/span><\/span>atingirem a extremidade fixa,<\/b><\/span><\/span><\/span> <\/b>sofrem reflex\u00e3o e retornam.<\/b><\/span><\/span><\/span> <\/b><\/p>\n

Assim, as <\/b><\/span><\/span><\/span>ondas incidentes e as refletidas se <\/b><\/span><\/span><\/span>superp\u00f5em<\/b><\/span><\/span><\/span>, <\/b><\/span><\/span><\/span>originando as<\/b><\/span><\/span><\/span> <\/b>ondas estacion\u00e1rias.<\/b><\/span><\/span><\/span><\/p>\n

Para <\/b><\/span><\/span><\/span>entender<\/b><\/span><\/span><\/span> como <\/b><\/span><\/span><\/span>surgem as ondas estacion\u00e1rias<\/b><\/span><\/span><\/span>, observe atentamente as sequ\u00eancias das <\/b><\/span><\/span><\/span>figuras abaixo,<\/b><\/span><\/span><\/span> onde, <\/b><\/span><\/span><\/span>em todas,<\/b><\/span><\/span><\/span> temos, <\/b><\/span><\/span><\/span>no mesmo instante<\/b><\/span><\/span><\/span>, nas <\/b><\/span><\/span><\/span>duas figuras da esquerda,<\/b><\/span><\/span><\/span> as <\/b><\/span><\/span><\/span>ondas se<\/b><\/span><\/span><\/span> <\/b>movendo em sentidos contr\u00e1rios<\/b><\/span><\/span><\/span> e, na <\/b><\/span><\/span><\/span>figura da direita, a superposi\u00e7\u00e3o das mesmas, nesse mesmo instante.<\/b><\/span><\/span><\/span>\"\"<\/p>\n

O <\/b><\/span><\/span><\/span>intervalo de tempo entre uma figura e outra \u00e9 de um quarto de per\u00edodo (T\/4),<\/b><\/span><\/span><\/span> ou seja, <\/b><\/span><\/span><\/span>entre cada intervalo a onda percorreu um quarto de comprimento de onda.<\/b><\/span><\/span><\/span><\/p>\n

No <\/b><\/span><\/span><\/span>instante t = 0,<\/b><\/span><\/span><\/span> as <\/b><\/span><\/span><\/span>duas ondas est\u00e3o exatamente superpostas e a onda resultante dessa superposi\u00e7\u00e3o tem amplitude 2A. (interfer\u00eancia construtiva).<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

No <\/b><\/span><\/span><\/span>instante t = T\/4,<\/b><\/span><\/span><\/span> <\/b>cada <\/b><\/span><\/span><\/span>uma delas <\/b><\/span><\/span><\/span>se moveu\u00a0\u03bb\/4 e suas configura\u00e7\u00f5es est\u00e3o nas duas figuras da<\/b><\/span><\/span><\/span> <\/b>esquerda.<\/b><\/span><\/span><\/span> Observe, na <\/b><\/span><\/span><\/span>figura da direita, que todos os pontos dessas ondas se anulam. (interfer\u00eancia destrutiva).<\/b><\/span><\/span><\/span><\/p>\n

No <\/b><\/span><\/span><\/span>instante t = T\/2,<\/b><\/span><\/span><\/span> a onda <\/b><\/span><\/span><\/span>resultante tem amplitude 2A.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

No <\/b><\/span><\/span><\/span>instante t = 3T\/2<\/b><\/span><\/span><\/span> essas ondas <\/b><\/span><\/span><\/span>novamente se anulam.<\/b><\/span><\/span><\/span><\/p>\n

No <\/b><\/span><\/span><\/span>instante t=T<\/b><\/span><\/span><\/span>, essas ondas <\/b><\/span><\/span><\/span>voltaram \u00e0 situa\u00e7\u00e3o inicial<\/b><\/span><\/span><\/span> e a partir <\/b><\/span><\/span><\/span>da\u00ed come\u00e7a a repeti\u00e7\u00e3o.<\/b><\/span><\/span><\/span>\"\"<\/p>\n

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

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

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

Observe que, em <\/b><\/span><\/span><\/span>todos os instantes,<\/b><\/span><\/span><\/span> os <\/b><\/span><\/span><\/span>pontos P, Q e R<\/b><\/span><\/span><\/span>, da <\/b><\/span><\/span><\/span>onda resultante n\u00e3o se moveram.<\/b><\/span><\/span><\/span> <\/b>Esses pontos, <\/b><\/span><\/span><\/span>sempre fixos<\/b><\/span><\/span><\/span> s\u00e3o chamados de\u00a0<\/b><\/span><\/span><\/span>nodos ou n\u00f3s<\/b><\/span><\/span><\/span>\u00a0e est\u00e3o em <\/b><\/span><\/span><\/span>interfer\u00eancia destrutiva.<\/b><\/span><\/span><\/span><\/p>\n

Observe tamb\u00e9m que, em <\/b><\/span><\/span><\/span>todos os instantes,<\/b><\/span><\/span><\/span> <\/b>todos<\/b><\/span><\/span><\/span> os <\/b><\/span><\/span><\/span>pontos compreendidos entre P e Q e entre Q e<\/b><\/span><\/span><\/span> <\/b><\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

Cada uma<\/b><\/span><\/span><\/span> dessas <\/b><\/span><\/span><\/span>amplitudes \u00e9 o dobro das amplitudes<\/b><\/span><\/span><\/span> das <\/b><\/span><\/span><\/span>ondas constituintes.<\/b><\/span><\/span><\/span><\/p>\n

Como os <\/b><\/span><\/span><\/span>n\u00f3s est\u00e3o em repouso,<\/b><\/span><\/span><\/span> <\/b>n\u00e3o pode haver passagem de energia por eles<\/b><\/span><\/span><\/span>, <\/b><\/span><\/span><\/span>n\u00e3o<\/b><\/span><\/span><\/span> havendo, ent\u00e3o, em uma <\/b><\/span><\/span><\/span>corda estacion\u00e1ria o <\/b><\/span><\/span><\/span>transporte de energia.<\/b><\/span><\/span><\/span><\/p>\n

Assim, <\/b><\/span><\/span><\/span>ondas estacion\u00e1rias<\/b><\/span><\/span><\/span> <\/b>n\u00e3o s\u00e3o ondas de propaga\u00e7\u00e3o,<\/b><\/span><\/span><\/span> mas sim, as <\/b><\/span><\/span><\/span>diferentes maneiras de vibra\u00e7\u00e3o de uma corda, membrana, etc.<\/b><\/span><\/span><\/span><\/p>\n

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

Interfer\u00eancia sonora<\/b><\/span><\/span><\/span><\/p>\n

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

Ocorre quando <\/b><\/span><\/span><\/span>duas ou mais ondas sonoras<\/b><\/span><\/span><\/span> se <\/b><\/span><\/span><\/span>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>= 100 Hz<\/b><\/span><\/span><\/span> e outra de <\/b><\/span><\/span><\/span>f<\/b><\/span><\/span><\/span>B <\/b><\/span><\/span><\/sub><\/span>= 110 Hz.<\/b><\/span><\/span><\/span><\/p>\n

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

\"\"<\/p>\n

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

A <\/b><\/span><\/span><\/span>freq\u00fc\u00eancia do batimento \u00e9 definida<\/b><\/span><\/span><\/span> 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 <\/b><\/span><\/span><\/span>utilizado na afina\u00e7\u00e3o de instrumentos musicais.<\/b><\/span><\/span><\/span> <\/b><\/p>\n

Se as <\/b><\/span><\/span><\/span>freq\u00fc\u00eancias da fonte afiadora e do instrumento forem diferentes, ouve-se o batimento.<\/b><\/span><\/span><\/span> <\/b><\/p>\n

A <\/b><\/span><\/span><\/span>freq\u00fc\u00eancia do batimento vai diminuindo<\/b><\/span><\/span><\/span> \u00e0 <\/b><\/span><\/span><\/span>medida que o instrumento vai sendo afinado<\/b><\/span><\/span><\/span> e, quando <\/b><\/span><\/span><\/span>desaparecer,<\/b><\/span><\/span><\/span> o <\/b><\/span><\/span><\/span>instrumento estar\u00e1 afinado.<\/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

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

\"\"<\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

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

Cada uma <\/b><\/span><\/span><\/span>das<\/b><\/span><\/span><\/span> amplitudes da onda estacion\u00e1ria<\/b><\/span><\/span><\/span> \u00e9 o <\/b><\/span><\/span><\/span>dobro das amplitudes das ondas constituintes.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Como <\/b><\/span><\/span><\/span>os n\u00f3s est\u00e3o em repouso,<\/b><\/span><\/span><\/span> <\/b>n\u00e3o <\/b><\/span><\/span><\/span>pode <\/b><\/span><\/span><\/span>haver passagem de energia por eles,<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>n\u00e3o havendo,<\/b><\/span><\/span><\/span> ent\u00e3o, em uma <\/b><\/span><\/span><\/span>onda\u00a0estacion\u00e1ria o transporte de energia.<\/b><\/span><\/span><\/span><\/p>\n

Assim, <\/b><\/span><\/span><\/span>ondas estacion\u00e1rias n\u00e3o s\u00e3o ondas de propaga\u00e7\u00e3o<\/b><\/span><\/span><\/span>, mas sim, as <\/b><\/span><\/span><\/span>diferentes maneiras de vibra\u00e7\u00e3o de uma corda, membrana, etc.<\/b><\/span><\/span><\/span><\/p>\n\n\n<\/colgroup>\n\n\n
<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

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

\"\"<\/p>\n

A <\/b><\/span><\/span><\/span>freq\u00fc\u00eancia do batimento \u00e9 definida<\/b><\/span><\/span><\/span> 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

\"\"<\/p>\n

O <\/b><\/span><\/span><\/span>fen\u00f4meno do batimento<\/b><\/span><\/span><\/span> \u00e9 muitas vezes <\/b><\/span><\/span><\/span>utilizado na afina\u00e7\u00e3o de instrumentos musicais.<\/b><\/span><\/span><\/span> <\/b><\/p>\n

Se as <\/b><\/span><\/span><\/span>freq\u00fc\u00eancias da fonte afiadora e do instrumento forem diferentes, ouve-se o batimento.<\/b><\/span><\/span><\/span> <\/b><\/p>\n

A <\/b><\/span><\/span><\/span>freq\u00fc\u00eancia do batimento vai diminuindo<\/b><\/span><\/span><\/span> \u00e0 <\/b><\/span><\/span><\/span>medida que o instrumento vai sendo afinado<\/b><\/span><\/span><\/span> e, quando <\/b><\/span><\/span><\/span>desaparecer,<\/b><\/span><\/span><\/span> o <\/b><\/span><\/span><\/span>instrumento estar\u00e1 afinado.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

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

\"\"<\/p>\n

\"\"<\/p>\n

Alguns exerc\u00edcios interessantes nos quais seria conveniente voc\u00ea analisar as resolu\u00e7\u00f5es:<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

02- (UFMS)<\/b><\/span><\/span><\/span> <\/b>A figura mostra <\/b><\/span><\/span><\/span>ondas estacion\u00e1rias<\/b><\/span><\/span><\/span> em uma <\/b><\/span><\/span><\/span>corda de comprimento 45cm,<\/b><\/span><\/span><\/span> de <\/b><\/span><\/span><\/span>densidade linear de massa\u00a0\u03bc = 6,2 g\/m,<\/b><\/span><\/span><\/span> com as duas <\/b><\/span><\/span><\/span>extremidades fixas,<\/b><\/span><\/span><\/span> e que est\u00e1 <\/b><\/span><\/span><\/span>vibrando a 450Hz.<\/b><\/span><\/span><\/span><\/p>\n

D\u00ea como <\/b><\/span><\/span><\/span>resposta a soma dos n\u00fameros correspondentes \u00e0s afirma\u00e7\u00f5es corretas.<\/b><\/span><\/span><\/span><\/p>\n

\u00c9 <\/b><\/span><\/span><\/span>correto afirmar<\/b><\/span><\/span><\/span> que:<\/b><\/span><\/span><\/span><\/p>\n

(01)<\/b><\/span><\/span><\/span> <\/b>todos os pontos<\/b><\/span><\/span><\/span> da corda <\/b><\/span><\/span><\/span>vibram <\/b><\/span><\/span><\/span>com a <\/b><\/span><\/span><\/span>mesma amplitude.<\/b><\/span><\/span><\/span><\/p>\n

(02)<\/b><\/span><\/span><\/span> <\/b>todos os pontos<\/b><\/span><\/span><\/span> da corda <\/b><\/span><\/span><\/span>vibram <\/b><\/span><\/span><\/span>com a <\/b><\/span><\/span><\/span>mesma freq\u00fc\u00eancia.<\/b><\/span><\/span><\/span><\/p>\n

(04)<\/b><\/span><\/span><\/span> o <\/b><\/span><\/span><\/span>comprimento de onda<\/b><\/span><\/span><\/span> na corda \u00e9 de <\/b><\/span><\/span><\/span>90 cm.<\/b><\/span><\/span><\/span>\"\"<\/p>\n

(08)<\/b><\/span><\/span><\/span> a <\/b><\/span><\/span><\/span>velocidade de propaga\u00e7\u00e3o<\/b><\/span><\/span><\/span> da onda na corda \u00e9 de <\/b><\/span><\/span><\/span>135m\/s.<\/b><\/span><\/span><\/span><\/p>\n

(16)<\/b><\/span><\/span><\/span> a <\/b><\/span><\/span><\/span>for\u00e7a tensora<\/b><\/span><\/span><\/span> na corda \u00e9 de <\/b><\/span><\/span><\/span>113N,<\/b><\/span><\/span><\/span> aproximadamente.<\/b><\/span><\/span><\/span><\/p>\n

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

(01)<\/b><\/span><\/span><\/span> <\/b>Errada.<\/b><\/span><\/span><\/span> O <\/b><\/span><\/span><\/span>movimento de cada ponto da onda estacion\u00e1ria \u00e9 somente na <\/b><\/span><\/span><\/span>vertical<\/b><\/span><\/span><\/span> e verifique na <\/b><\/span><\/span><\/span>figura abaixo<\/b><\/span><\/span><\/span> que os <\/b><\/span><\/span><\/span>pontos A, A<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>\u00a0e A<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span>\u00a0<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/sub><\/span>tem <\/b><\/span><\/span><\/span>amplitudes diferentes no seu \u201csobe e desce\u201d completo.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

(02)<\/b><\/span><\/span><\/span> <\/b>Correta.<\/b><\/span><\/span><\/span> Esta <\/b><\/span><\/span><\/span>freq\u00fc\u00eancia de 450Hz<\/b><\/span><\/span><\/span> \u00e9 a <\/b><\/span><\/span><\/span>freq\u00fc\u00eancia das ondas que se superp\u00f5e<\/b><\/span><\/span><\/span> e \u00e9 a mesma <\/b><\/span><\/span><\/span>para todos os pontos da corda que vibram.<\/b><\/span><\/span><\/span><\/p>\n

(04)<\/b><\/span><\/span><\/span> <\/b>Errada.<\/b><\/span><\/span><\/span> <\/b>3\u03bb\/2 = 45<\/b><\/span><\/span><\/span>\u00a0 \"\"\u00a0\u00a0<\/b><\/span><\/span><\/span>\u03bb = 30 cm.<\/b><\/span><\/span><\/span><\/p>\n

(08)<\/b><\/span><\/span><\/span> <\/b>Correta.<\/b><\/span><\/span><\/span> <\/b>V = \u03bbf<\/b><\/span><\/span><\/span>\u00a0 \"\"\u00a0 <\/b><\/span><\/span><\/span>V <\/b><\/span><\/span><\/span>= 30.450 = <\/b><\/span><\/span><\/span>13.500 cm\/s = 135m\/s.<\/b><\/span><\/span><\/span><\/p>\n

(16)<\/b><\/span><\/span><\/span> <\/b>Correta.<\/b><\/span><\/span><\/span>\u00a0 <\/b><\/span><\/span><\/span>V=\u221a(F\/\u03bc)<\/b><\/span><\/span><\/span>\u00a0 \"\"\u00a0 135 = \u221a(F\/6,2.10<\/b><\/span><\/span><\/span>-3<\/b><\/span><\/span><\/sup><\/span>)\u00a0 \"\"\u00a0 (135)<\/b><\/span><\/span><\/span>2 <\/b><\/span><\/span><\/sup><\/span>= (F\/6,2.10<\/b><\/span><\/span><\/span>-3<\/b><\/span><\/span><\/sup><\/span>)<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>\u00a0 \"\"\u00a0 18.225 = F\/0,0062\u00a0 \"\"\u00a0 <\/b><\/span><\/span><\/span><\/p>\n

F = 112,995 N.<\/b><\/span><\/span><\/span><\/p>\n

Soma = (02 + 08 +16) = 26<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

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

Aplicando a <\/b><\/span><\/span><\/span>equa\u00e7\u00e3o fundamental da ondulat\u00f3ria<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>para a:<\/b><\/span><\/span><\/span> <\/b><\/p>\n

R\u00e1dio da cidade<\/b><\/span><\/span><\/span>\u00a0 \"\"\u00a0 <\/b><\/span><\/span><\/span>V = <\/b><\/span><\/span><\/span>\u03bb<\/b><\/span><\/span><\/span><\/span>c<\/b><\/span><\/span><\/sub><\/span>.f<\/b><\/span><\/span><\/span>c<\/b><\/span><\/span><\/sub><\/span>. \u00a0<\/b><\/span><\/span><\/span><\/p>\n

R\u00e1dio pirata<\/b><\/span><\/span><\/span>\u00a0 \"\"\u00a0 <\/b><\/span><\/span><\/span>V = <\/b><\/span><\/span><\/span>\u03bb<\/b><\/span><\/span><\/span><\/span>p<\/b><\/span><\/span><\/sub><\/span>.f<\/b><\/span><\/span><\/span>p<\/b><\/span><\/span><\/sub><\/span>.\u00a0<\/b><\/span><\/span><\/span> <\/b><\/p>\n

Como a <\/b><\/span><\/span><\/span>velocidade (V) de propaga\u00e7\u00e3o da onda \u00e9 a mesma,<\/b><\/span><\/span><\/span> pois se trata <\/b><\/span><\/span><\/span>do mesmo meio de propaga\u00e7\u00e3o (ar),<\/b><\/span><\/span><\/span> e as <\/b><\/span><\/span><\/span>frequ\u00eancias (f), pelo enunciado, s\u00e3o iguais<\/b><\/span><\/span><\/span>, os <\/b><\/span><\/span><\/span>comprimentos onda (\u03bb) tamb\u00e9m o ser\u00e3o.<\/b><\/span><\/span><\/span><\/p>\n

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

\"\"<\/p>\n

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

O <\/b><\/span><\/span><\/span>ponto 2 da corda \u00e9 um n\u00f3<\/b><\/span><\/span><\/span> (ou nodo) da <\/b><\/span><\/span><\/span>onda estacion\u00e1ria <\/b><\/span><\/span><\/span>e <\/b><\/span><\/span><\/span>permanece fixo<\/b><\/span><\/span><\/span>\u00a0. <\/b><\/span><\/span><\/span><\/p>\n

Os <\/b><\/span><\/span><\/span>pontos 1 e 3<\/b><\/span><\/span><\/span> possuem <\/b><\/span><\/span><\/span>velocidade nula<\/b><\/span><\/span><\/span> nas extremidades superiores e inferiores<\/b><\/span><\/span><\/span> e <\/b><\/span><\/span><\/span>velocidades <\/b><\/span><\/span><\/span>m\u00e1ximas <\/b><\/span><\/span><\/span>quando <\/b><\/span><\/span><\/span>passam pela centro <\/b><\/span><\/span><\/span>(onde est\u00e3o esses pontos),\u00a0 <\/b><\/span><\/span><\/span>apenas que eles<\/b><\/span><\/span><\/span> <\/b>possuem velocidades de sentidos contr\u00e1rios,<\/b><\/span><\/span><\/span> ou seja, enquanto um <\/b><\/span><\/span><\/span>est\u00e1 subindo o outro estar\u00e1 descendo\u00a0.<\/b><\/span><\/span><\/span><\/p>\n

R-\u00a0 D.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

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

Observe nas <\/b><\/span><\/span><\/span>figuras abaixo as ondas estacion\u00e1rias<\/b><\/span><\/span><\/span> formadas em <\/b><\/span><\/span><\/span>cada caso\u00a0:<\/b><\/span><\/span><\/span><\/p>\n

Primeira figura<\/b><\/span><\/span><\/span> \"\" <\/b><\/span><\/span><\/span>\u03bb<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>\/2 = L<\/b><\/span><\/span><\/span>\u00a0 \"\"\u00a0 \u03b3 <\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>= 2L\u00a0 \"\"\u00a0 V<\/b><\/span><\/span><\/span>1 <\/b><\/span><\/span><\/sub><\/span>= \u03b3<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>.f<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>\u00a0 \"\"\u00a0 <\/b><\/span><\/span><\/span>V<\/b><\/span><\/span><\/span>1 <\/b><\/span><\/span><\/sub><\/span>= 2L.f<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span> (I).<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Segunda figura<\/b><\/span><\/span><\/span> \"\" <\/b><\/span><\/span><\/span>\u03b3<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span>\/2 = L\/2<\/b><\/span><\/span><\/span> \"\"\u00a0 <\/b><\/span><\/span><\/span>\u03b3<\/b><\/span><\/span><\/span>2 <\/b><\/span><\/span><\/sub><\/span>= L<\/b><\/span><\/span><\/span>\u00a0 \"\"\u00a0 <\/b><\/span><\/span><\/span>V<\/b><\/span><\/span><\/span>2 <\/b><\/span><\/span><\/sub><\/span>= \u03b3<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span>.f<\/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>= L.f<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span>\u00a0(II).<\/b><\/span><\/span><\/span>\u00a0 <\/b><\/span><\/span><\/span><\/p>\n

Como a <\/b><\/span><\/span><\/span>velocidade de propaga\u00e7\u00e3o em cada caso \u00e9 a mesma<\/b><\/span><\/span><\/span> (mesmo meio, ar)\u00a0 \"\"\u00a0 <\/b><\/span><\/span><\/span>V<\/b><\/span><\/span><\/span>1 <\/b><\/span><\/span><\/sub><\/span>= V<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span>\u00a0 \"\"\u00a0 <\/b><\/span><\/span><\/span>I = II<\/b><\/span><\/span><\/span>\u00a0 \"\" 2Lf<\/b><\/span><\/span><\/span>1 <\/b><\/span><\/span><\/sub><\/span>= Lf<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span>\u00a0 —\u00a0 2.220 = f<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span>\u00a0 \"\"\u00a0 <\/b><\/span><\/span><\/span>f<\/b><\/span><\/span><\/span>2 <\/b><\/span><\/span><\/sub><\/span>= 440 Hz.\u00a0<\/b><\/span><\/span><\/span>\u00a0\u00a0<\/b><\/span><\/span><\/span><\/p>\n

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

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

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

Ondas Estacion\u00e1rias Forma\u00e7\u00e3o de ondas estacion\u00e1rias Obtemos\u00a0ondas estacion\u00e1rias\u00a0pela superposi\u00e7\u00e3o de duas ondas id\u00eanticas, de mesma amplitude, mesma frequ\u00eancia, mesmo comprimento de onda e que se movem na mesma dire\u00e7\u00e3o e sentidos opostos. Considere uma corda fixa em uma das extremidades e na outra uma fonte produz ondas peri\u00f3dicas que, ao atingirem a extremidade fixa, sofrem reflex\u00e3o e retornam. Assim, as<\/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-2377","page","type-page","status-publish","hentry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/2377","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=2377"}],"version-history":[{"count":2,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/2377\/revisions"}],"predecessor-version":[{"id":2383,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/2377\/revisions\/2383"}],"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=2377"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}