{"id":2345,"date":"2016-08-01T23:34:06","date_gmt":"2016-08-01T23:34:06","guid":{"rendered":"http:\/\/fisicaevestibular.com.br\/novo\/?page_id=2345"},"modified":"2024-08-23T14:58:17","modified_gmt":"2024-08-23T14:58:17","slug":"tubos-sonoros","status":"publish","type":"page","link":"https:\/\/fisicaevestibular.com.br\/novo\/ondulatoria\/acustica\/tubos-sonoros\/","title":{"rendered":"Tubos sonoros"},"content":{"rendered":"

Tubos Sonoros<\/b><\/span><\/span><\/span><\/p>\n

C\u00e1lculo da velocidade de propaga\u00e7\u00e3o do som no ar<\/b><\/span><\/span><\/span><\/p>\n

Considere um <\/b><\/span><\/span><\/span>diapas\u00e3o (fonte sonora) <\/b><\/span><\/span><\/span>produzindo <\/b><\/span><\/span><\/span>sons <\/b><\/span><\/span><\/span>sobre a <\/b><\/span><\/span><\/span>extremidade aberta de um tubo de vidro<\/b><\/span><\/span><\/span> de <\/b><\/span><\/span><\/span>comprimento L<\/b><\/span><\/span><\/span>, sendo <\/b><\/span><\/span><\/span>preenchido vagarosamente com \u00e1gua, <\/b><\/span><\/span><\/span>o que conseguimos <\/b><\/span><\/span><\/span>elevando o reservat\u00f3rio R de \u00e1gua, mantendo assim os n\u00edveis de R e do tubo aberto (figura abaixo)<\/b><\/span><\/span><\/span>\"\"<\/p>\n

Quando o <\/b><\/span><\/span><\/span>reservat\u00f3rio \u00e9 levantado, <\/b><\/span><\/span><\/span>o <\/b><\/span><\/span><\/span>n\u00edvel da \u00e1gua no tubo aberto vai subindo <\/b><\/span><\/span><\/span>e assim, a <\/b><\/span><\/span><\/span>intensidade do som emitido pelo diapas\u00e3o \u00e9 refor\u00e7ado.<\/b><\/span><\/span><\/span><\/p>\n

Isso ocorre porque, no <\/b><\/span><\/span><\/span>interior do tubo, as ondas sonoras emitidas pelo diapas\u00e3o sofrem interfer\u00eancia com as ondas refletidas na superf\u00edcie da \u00e1gua, <\/b><\/span><\/span><\/span>dando <\/b><\/span><\/span><\/span>origem a ondas estacion\u00e1rias <\/b><\/span><\/span><\/span>que, para <\/b><\/span><\/span><\/span>determinadas alturas da coluna de ar refor\u00e7ar\u00e1 o som proveniente do diapas\u00e3o.<\/b><\/span><\/span><\/span> <\/b><\/p>\n

O <\/b><\/span><\/span><\/span>som ter\u00e1 intensidade m\u00e1xima quando cada compress\u00e3o, refletida pela \u00e1gua, volta para a abertura <\/b><\/span><\/span><\/span>justamente quando a <\/b><\/span><\/span><\/span>pr\u00f3xima est\u00e1 saindo do diapas\u00e3o e assim elas se refor\u00e7am mutuamente. <\/b><\/span><\/span><\/span><\/p>\n

O diapas\u00e3o e a coluna de ar no interior do tubo est\u00e3o em resson\u00e2ncia<\/b><\/span><\/span><\/span><\/p>\n

O <\/b><\/span><\/span><\/span>primeiro refor\u00e7o <\/b><\/span><\/span><\/span>ocorre quando a <\/b><\/span><\/span><\/span>altura da coluna de \u00e1gua <\/b><\/span><\/span><\/span>\u00e9 <\/b><\/span><\/span><\/span>um quarto do comprimento de onda do som \u00a0<\/b><\/span><\/span><\/span>\"\"<\/p>\n

Os <\/b><\/span><\/span><\/span>sucessivos refor\u00e7os sonoros ocorrem sempre<\/b><\/span><\/span><\/span> que na <\/b><\/span><\/span><\/span>extremidade aberta do tubo <\/b><\/span><\/span><\/span>surgir um <\/b><\/span><\/span><\/span>ventre (vibra\u00e7\u00e3o m\u00e1xima das part\u00edculas de ar)<\/b><\/span><\/span><\/span>. <\/b><\/span><\/span><\/span><\/p>\n

A <\/b><\/span><\/span><\/span>extremidade fechada<\/b><\/span><\/span><\/span> \u00e9 <\/b><\/span><\/span><\/span>sempre um n\u00f3 (vibra\u00e7\u00e3o nula das part\u00edculas de ar).<\/b><\/span><\/span><\/span><\/p>\n

Este processo \u00e9 <\/b><\/span><\/span><\/span>utilizado na determina\u00e7\u00e3o da velocidade de propaga\u00e7\u00e3o do som no ar<\/b><\/span><\/span><\/span>, conhecendo a <\/b><\/span><\/span><\/span>freq\u00fc\u00eancia f do diapas\u00e3o e medindo-se a altura da coluna de ar <\/b><\/span><\/span><\/span>(diferen\u00e7a do n\u00edvel da \u00e1gua) <\/b><\/span><\/span><\/span>entre duas intensidades m\u00e1ximas de som consecutivas, <\/b><\/span><\/span><\/span>que nos <\/b><\/span><\/span><\/span>fornece<\/b><\/span><\/span><\/span> o <\/b><\/span><\/span><\/span>comprimento de onda\u00a0\u03bb.<\/b><\/span><\/span><\/span><\/p>\n

A <\/b><\/span><\/span><\/span>dist\u00e2ncia d entre dois ventres (m\u00e1ximos) consecutivos <\/b><\/span><\/span><\/span>fornece\u00a0<\/b><\/span><\/span><\/span>\u03bb<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>(d= \u03bb \/2).<\/b><\/span><\/span><\/span> <\/b><\/p>\n

Assim, <\/b><\/span><\/span><\/span>conhecidos V e\u00a0\u03bb, <\/b><\/span><\/span><\/span>determinamos a <\/b><\/span><\/span><\/span>velocidade do som no ar <\/b><\/span><\/span><\/span>atrav\u00e9s da <\/b><\/span><\/span><\/span>equa\u00e7\u00e3o fundamental da ondulat\u00f3ria<\/b><\/span><\/span><\/span><\/p>\n

V = \u03bb f.<\/b><\/span><\/span><\/span><\/p>\n

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

Tubo fechado numa das extremidades<\/b><\/span><\/span><\/span><\/p>\n

Seu <\/b><\/span><\/span><\/span>princ\u00edpio de funcionamento \u00e9 o mesmo do processo acima <\/b><\/span><\/span><\/span>onde o <\/b><\/span><\/span><\/span>n\u00edvel da \u00e1gua representa a <\/b><\/span><\/span><\/span>extremidade fechada que \u00e9 sempre um n\u00f3. <\/b><\/span><\/span><\/span><\/p>\n

A <\/b><\/span><\/span><\/span>extremidade aberta \u00e9 sempre um ventre.<\/b><\/span><\/span><\/span><\/p>\n

Nestes instrumentos, uma <\/b><\/span><\/span><\/span>coluna de ar \u00e9 posta a vibrar ao soprar-se uma das extremidades do tubo, chamada embocadura,<\/b><\/span><\/span><\/span> pr\u00f3xima \u00e0 <\/b><\/span><\/span><\/span>extremidade aberta <\/b><\/span><\/span><\/span>sendo que <\/b><\/span><\/span><\/span>a outra extremidade \u00e9 fechada.<\/b><\/span><\/span><\/span><\/p>\n

Embocadura <\/b><\/span><\/span><\/span>\u00e9 a <\/b><\/span><\/span><\/span>forma apropriada de usar a boca e a l\u00edngua <\/b><\/span><\/span><\/span>contra <\/b><\/span><\/span><\/span>o bocal de um instrumento de sopro. <\/b><\/span><\/span><\/span><\/p>\n

Na extremidade aberta <\/b><\/span><\/span><\/span>um <\/b><\/span><\/span><\/span>jato\u00a0de ar soprado \u00e9 comprimido <\/b><\/span><\/span><\/span>por um <\/b><\/span><\/span><\/span>cal\u00e7o <\/b><\/span><\/span><\/span>para depois <\/b><\/span><\/span><\/span>colidir\u00a0contra um corte em diagonal (orif\u00edcio), bem abaixo, na parede do tubo.<\/b><\/span><\/span><\/span><\/p>\n

\"\"Assim, o <\/b><\/span><\/span><\/span>jato\u00a0de ar sofre turbilhonamentos e varia\u00e7\u00f5es de press\u00e3o que\u00a0o for\u00e7am a ir<\/b><\/span><\/span><\/span>, <\/b><\/span><\/span>alternadamente <\/b><\/span><\/span><\/span>ora para fora, ora para dentro do tubo. <\/b><\/span><\/span><\/span><\/p>\n

Dessa maneira, a <\/b><\/span><\/span><\/span>coluna gasosa interna do tubo \u00e9 golpeada interminentemente<\/b><\/span><\/span><\/span>, <\/b><\/span><\/span>dando <\/b><\/span><\/span><\/span>origem <\/b><\/span><\/span><\/span>a uma <\/b><\/span><\/span><\/span>onda longitudinal que se\u00a0propaga no interior do tubo<\/b><\/span><\/span><\/span>, com <\/b><\/span><\/span><\/span>n\u00f3s e ventres, <\/b><\/span><\/span><\/span>provocando a <\/b><\/span><\/span><\/span><\/span><\/span><\/span>emiss\u00e3o do som.<\/b><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

Comprimentos de onda e frequ\u00eancias para um tubo fechado<\/b><\/span><\/span><\/span><\/p>\n

A seguir temos os <\/b><\/span><\/span><\/span>sucessivos comprimentos de onda e freq\u00fc\u00eancias<\/b><\/span><\/span><\/span> para um <\/b><\/span><\/span><\/span>tubo fechado <\/b><\/span><\/span><\/span>numa das <\/b><\/span><\/span><\/span>extremidades, de comprimento <\/b><\/span><\/span><\/span>L<\/b><\/span><\/span><\/span>. <\/b><\/span><\/span><\/span><\/p>\n

V<\/b><\/span><\/span><\/span> representa os ventres <\/b><\/span><\/span><\/span>(pontos de vibra\u00e7\u00e3o m\u00e1xima<\/b><\/span><\/span><\/span>) e <\/b><\/span><\/span><\/span>N<\/b><\/span><\/span><\/span> os n\u00f3s <\/b><\/span><\/span><\/span>(pontos de vibra\u00e7\u00e3o nula).<\/b><\/span><\/span><\/span><\/p>\n

Devido \u00e0s <\/b><\/span><\/span><\/span>configura\u00e7\u00f5es (simetria) das ondas em seu interior<\/b><\/span><\/span><\/span>, <\/b><\/span><\/span><\/span>tubos abertos <\/b><\/span><\/span><\/span>s\u00f3 fornecem <\/b><\/span><\/span><\/span>harm\u00f4nicos impares.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Express\u00f5es gen\u00e9ricas para n harm\u00f4nicos:<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Tubo aberto nas duas extremidades<\/b><\/span><\/span><\/span><\/p>\n

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

Como<\/b><\/span><\/span><\/span> ambas as extremidades s\u00e3o abertas,<\/b><\/span><\/span><\/span> em <\/b><\/span><\/span><\/span>cada uma delas devemos ter ventres.<\/b><\/span><\/span><\/span><\/p>\n

Seus <\/b><\/span><\/span><\/span>harm\u00f4nicos, freq\u00fc\u00eancias e comprimentos de onda <\/b><\/span><\/span><\/span>s\u00e3o os seguintes.<\/b><\/span><\/span><\/span><\/p>\n

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

\"\"<\/p>\n

\"\"<\/p>\n

Express\u00f5es gen\u00e9ricas para n harm\u00f4nicos:<\/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

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

\u00c9 <\/b><\/span><\/span><\/span>poss\u00edvel <\/b><\/span><\/span><\/span>visualizar atrav\u00e9s de mont\u00edculos de p\u00f3 de corti\u00e7a <\/b><\/span><\/span><\/span>a <\/b><\/span><\/span><\/span>localiza\u00e7\u00e3o de<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>n\u00f3s <\/b><\/span><\/span><\/span>(regi\u00e3o isenta de vibra\u00e7\u00e3o, e de som) no <\/b><\/span><\/span><\/span>sistema de ondas estacion\u00e1rias que se estabelece como resultado da superposi\u00e7\u00e3o da onda sonora direta e a onda sonora refletida.<\/b><\/span><\/span><\/span><\/p>\n

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

\"\"<\/p>\n

Comprimentos de onda e frequ\u00eancias para um tubo fechado<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

Para <\/b><\/span><\/span><\/span>produzir sons diferentes <\/b><\/span><\/span><\/span>(notas diferentes) num <\/b><\/span><\/span><\/span>instrumento de sopro <\/b><\/span><\/span><\/span>(por exemplo, flauta doce, tubo fechado), ao <\/b><\/span><\/span><\/span>mesmo tempo <\/b><\/span><\/span><\/span>que o m\u00fasico <\/b><\/span><\/span><\/span>sobra no bocal, seus dedos tampam e destampam os orif\u00edcios distribuidos pelo corpo da flauta.<\/b><\/span><\/span><\/span><\/p>\n

Esse comportamento <\/b><\/span><\/span><\/span>provoca mudan\u00e7as no comprimento da onda estacion\u00e1ria<\/b><\/span><\/span><\/span>, que corresponde ao <\/b><\/span><\/span><\/span>comprimento da coluna de ar no interior da flauta, <\/b><\/span><\/span><\/span>o que influi tamb\u00e9m na <\/b><\/span><\/span><\/span>varia\u00e7\u00e3o da frequ\u00eancia do som obtido, produzindo maior variedade de sons (notas) emitidos.<\/b><\/span><\/span><\/span>\"\"<\/p>\n

\"\"<\/p>\n

Comprimentos de onda e frequ\u00eancias para um tubo aberto nas duas extremidades<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

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

\"\"<\/p>\n

Nos <\/b><\/span><\/span><\/span>instrumentos mais simples <\/b><\/span><\/span><\/span>como <\/b><\/span><\/span><\/span>o berrante e a corneta<\/b><\/span><\/span><\/span>, com <\/b><\/span><\/span><\/span>ambas as extremidade abertas<\/b><\/span><\/span><\/span>, o <\/b><\/span><\/span><\/span>comprimento do tubo \u00e9 fixo.\u00a0<\/b><\/span><\/span><\/span><\/p>\n

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

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

Mas, para <\/b><\/span><\/span><\/span>se obter uma quantidade maior de freq\u00fc\u00eancias, altera-se o comprimento dos tubos <\/b><\/span><\/span><\/span>(abertos ou fechados). <\/b><\/span><\/span><\/span><\/p>\n

Alguns <\/b><\/span><\/span><\/span>possuem furos que podem ser tampados com os dedos<\/b><\/span><\/span><\/span> (flauta simples) ou <\/b><\/span><\/span><\/span>por meio de mecanismos de chaves \u2018v\u00e1lvulas\u2019, (saxofone, flauta transversal, etc.)<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

A <\/b><\/span><\/span><\/span>exist\u00eancia<\/b><\/span><\/span><\/span> de <\/b><\/span><\/span><\/span> furo nos tubos <\/b><\/span><\/span><\/span>(como \u00e9 o caso da flauta, saxofone, clarinetes, pist\u00e3o, \u00f3rg\u00e3os antigos, etc), <\/b><\/span><\/span><\/span>acarretar\u00e1 na forma\u00e7\u00e3o de um VENTRE naqueles locais.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

A <\/b><\/span><\/span><\/span>velocidade de propaga\u00e7\u00e3o da onda sonora na coluna de ar <\/b><\/span><\/span><\/span>presente no <\/b><\/span><\/span><\/span>interior de qualquer tubo <\/b><\/span><\/span><\/span>\u00e9 <\/b><\/span><\/span><\/span>depende<\/b><\/span><\/span><\/span> da <\/b><\/span><\/span><\/span>temperatura absoluta do g\u00e1s, pois V = \"\". <\/b><\/span><\/span><\/span><\/p>\n

Assim, uma <\/b><\/span><\/span><\/span>varia\u00e7\u00e3o de temperatura pode alterar a afina\u00e7\u00e3o de um instrumento musical de sopro. <\/b><\/span><\/span><\/span>Por exemplo<\/b><\/span><\/span><\/span>, <\/b><\/span><\/span><\/span>um <\/b><\/span><\/span><\/span>aumento de temperatura<\/b><\/span><\/span><\/span>, causa um <\/b><\/span><\/span><\/span>aumento na velocidade de propaga\u00e7\u00e3o do som (V \u00e9 diretamente proporcional \u00e0 \"\" <\/b><\/span><\/span><\/span>e, assim, o tubo <\/b><\/span><\/span><\/span>emitir\u00e1 um harm\u00f4nico fundamental de maior <\/b><\/span><\/span><\/span>freq\u00fc\u00eancia, portanto <\/b><\/span><\/span><\/span>mais agudo. <\/b><\/span><\/span><\/span><\/p>\n

Os <\/b><\/span><\/span><\/span>instrumentos de corda <\/b><\/span><\/span><\/span>tamb\u00e9m <\/b><\/span><\/span><\/span>s\u00e3o afetados pela varia\u00e7\u00e3o de temperatura <\/b><\/span><\/span><\/span>que pode <\/b><\/span><\/span><\/span>afetar<\/b><\/span><\/span><\/span> o <\/b><\/span><\/span><\/span>comprimento das cordas<\/b><\/span><\/span><\/span> o <\/b><\/span><\/span><\/span>que alterar\u00e1 a for\u00e7a tensora nas mesmas<\/b><\/span><\/span><\/span>, desafinando os instrumentos. <\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Quando voc\u00ea coloca uma <\/b><\/span><\/span><\/span>concha junto ao ouvido, ouve um “ru\u00eddo de mar”<\/b><\/span><\/span><\/span>, como muita gente diz. <\/b><\/span><\/span><\/span><\/p>\n

Na verdade, esse som \u00e9 <\/b><\/span><\/span><\/span>produzido por qualquer cavidade colocada junto ao seu ouvido <\/b><\/span><\/span><\/span>como, por exemplo, a <\/b><\/span><\/span><\/span>sua pr\u00f3pria m\u00e3o em forma de concha ou um canudo. <\/b><\/span><\/span><\/span>\"\"<\/p>\n

A <\/b><\/span><\/span><\/span>verdadeira<\/b><\/span><\/span><\/span> origem desse som, na realidade, s\u00e3o as <\/b><\/span><\/span><\/span>m\u00faltiplas reflex\u00f5es de sons do pr\u00f3prio meio ambiente, no interior da concha, de sua m\u00e3o ou do canudo.<\/b><\/span><\/span><\/span><\/p>\n

\u00a0Assim, voc\u00ea est\u00e1 <\/b><\/span><\/span><\/span>apenas ouvindo a todos os sons que est\u00e3o ao seu redor.<\/b><\/span><\/span><\/span><\/p>\n

A <\/b><\/span><\/span><\/span>forma de concha <\/b><\/span><\/span><\/span>funciona como um <\/b><\/span><\/span><\/span>amplificador<\/b><\/span><\/span><\/span> do <\/b><\/span><\/span><\/span>som ambiente. <\/b><\/span><\/span><\/span>\u00c9 por isso que <\/b><\/span><\/span><\/span>alguns anfiteatros ao ar livre t\u00eam este formato e tamb\u00e9m os auto falantes. <\/b><\/span><\/span><\/span><\/p>\n

Encostando a <\/b><\/span><\/span><\/span>concha na orelha<\/b><\/span><\/span><\/span>, o <\/b><\/span><\/span><\/span>ar <\/b><\/span><\/span><\/span>que passar por ela vai <\/b><\/span><\/span><\/span>bater e voltar nas suas superf\u00edcies internas curvadas <\/b><\/span><\/span><\/span>e, esta <\/b><\/span><\/span><\/span>resson\u00e2ncia do ar acaba criando o som que a gente percebe.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Se voc\u00ea quizer <\/b><\/span><\/span><\/span>aprofundar<\/b><\/span><\/span><\/span> seu <\/b><\/span><\/span><\/span>conhecimento <\/b><\/span><\/span><\/span>sobre <\/b><\/span><\/span><\/span>tubos sonoros<\/b><\/span><\/span><\/span>, analise atentamente as <\/b><\/span><\/span><\/span>resolu\u00e7\u00f5es dos exerc\u00edcios de n\u00fameros: 02; 03; 08; 10; 11; 17; 21 e 24.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Resolu\u00e7\u00f5es de alguns exerc\u00edcios interessantes:<\/b><\/span><\/span><\/span><\/p>\n

01–(ITA-SP)<\/b><\/span><\/span><\/span> <\/b>Um <\/b><\/span><\/span><\/span>tubo sonoro aberto <\/b><\/span><\/span><\/span>em <\/b><\/span><\/span><\/span>uma das extremidades e fechado na outra <\/b><\/span><\/span><\/span>apresenta uma <\/b><\/span><\/span><\/span>freq\u00fc\u00eancia fundamental de 200Hz. <\/b><\/span><\/span><\/span><\/p>\n

Sabendo-se que o <\/b><\/span><\/span><\/span>intervalo de freq\u00fc\u00eancias aud\u00edveis <\/b><\/span><\/span><\/span>\u00e9 aproximadamente de <\/b><\/span><\/span><\/span>20Hz a 16.000Hz, determine\u00a0<\/b><\/span><\/span><\/span> o <\/b><\/span><\/span><\/span>n\u00famero<\/b><\/span><\/span><\/span> de <\/b><\/span><\/span><\/span>freq\u00fc\u00eancias aud\u00edveis emitidas pelo tubo.<\/b><\/span><\/span><\/span><\/p>\n

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

Tubo fechado <\/b><\/span><\/span><\/span>s\u00f3 tem <\/b><\/span><\/span><\/span>harm\u00f4nicos \u00edmpares <\/b><\/span><\/span><\/span>a <\/b><\/span><\/span><\/span>freq\u00fc\u00eancia fundamental <\/b><\/span><\/span><\/span>desse tubo \u00e9 <\/b><\/span><\/span><\/span>f<\/b><\/span><\/span><\/span>1 <\/b><\/span><\/span><\/sub><\/span>= 200Hz.\u00a0 <\/b><\/span><\/span><\/span><\/p>\n

Da <\/b><\/span><\/span><\/span>teoria<\/b><\/span><\/span><\/span> para <\/b><\/span><\/span><\/span>tubos fechados \"\" <\/b><\/span><\/span><\/span> f<\/b><\/span><\/span><\/span>n <\/b><\/span><\/span><\/sub><\/span>= nf<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>\u00a0(n = 1,3,5,…)\u00a0 \"\"\u00a0 Quando o <\/b><\/span><\/span><\/span>som for de 16.000Hz, <\/b><\/span><\/span><\/span>o <\/b><\/span><\/span><\/span>harm\u00f4nico n <\/b><\/span><\/span><\/span>\u00e9 de\u00a0 \"\"\u00a0 <\/b><\/span><\/span><\/span>16.000 =n.200\u00a0 \"\"<\/b><\/span><\/span><\/span>\u00a0 <\/b><\/span><\/span><\/span>n = 80. <\/b><\/span><\/span><\/span><\/p>\n

Mas, <\/b><\/span><\/span><\/span>80 \u00e9 par <\/b><\/span><\/span><\/span>e o tubo <\/b><\/span><\/span><\/span>n\u00e3o possui esse harm\u00f4nico mas sim, o primeiro \u00edmpar anterior que \u00e9 o 79.<\/b><\/span><\/span><\/span><\/p>\n

O <\/b><\/span><\/span><\/span>primeiro harm\u00f4nico \u00e9 n = 1. <\/b><\/span><\/span><\/span><\/p>\n

Assim, <\/b><\/span><\/span><\/span>temos que determinar o n\u00famero de harm\u00f4nicos \u00edmpares compreendidos <\/b><\/span><\/span><\/span>entre <\/b><\/span><\/span><\/span>1 e 79\u00a0 <\/b><\/span><\/span><\/span>que \u00e9 <\/b><\/span><\/span><\/span>38.<\/b><\/span><\/span><\/span> Portanto o <\/b><\/span><\/span><\/span>n\u00famero de freq\u00fc\u00eancias aud\u00edveis \u00e9 de 40<\/b><\/span><\/span><\/span>.\u00a0\u00a0 <\/b><\/span><\/span><\/span><\/p>\n

02-(FUVEST-SP)<\/b><\/span><\/span><\/span> <\/b>Um <\/b><\/span><\/span><\/span>m\u00fasico sopra a extremidade aberta de um tubo de 25cm de comprimento, fechado<\/b><\/span><\/span><\/span> na <\/b><\/span><\/span><\/span>outra extremidade, <\/b><\/span><\/span><\/span>emitindo um <\/b><\/span><\/span><\/span>som na freq\u00fc\u00eancia f = 1.700Hz. <\/b><\/span><\/span><\/span><\/p>\n

A <\/b><\/span><\/span><\/span>velocidade<\/b><\/span><\/span><\/span> do som no <\/b><\/span><\/span><\/span>ar <\/b><\/span><\/span><\/span>nas condi\u00e7\u00f5es do experimento \u00e9 <\/b><\/span><\/span><\/span>V=340m\/s. <\/b><\/span><\/span><\/span>\"\"<\/p>\n

Dos <\/b><\/span><\/span><\/span>diagramas abaixo,<\/b><\/span><\/span><\/span> aquele que <\/b><\/span><\/span><\/span>melhor representa a amplitude de deslocamento da onda sonora estacion\u00e1ria no tubo pelo sopro do m\u00fasico, <\/b><\/span><\/span><\/span>\u00e9:<\/b><\/span><\/span><\/span><\/p>\n

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

C\u00e1lculo de <\/b><\/span><\/span><\/span>n <\/b><\/span><\/span><\/span>quando <\/b><\/span><\/span><\/span>a frequ\u00eancia for de f = 1700 Hz <\/b><\/span><\/span><\/span>para o tubo fechado numa extremidade de <\/b><\/span><\/span><\/span>comprimento L = 25 cm = 0,25 m \"\"<\/b><\/span><\/span><\/span> <\/b>f<\/b><\/span><\/span><\/span>n <\/b><\/span><\/span><\/sub><\/span>= nV\/2<\/b><\/span><\/span><\/span>L\u00a0 \"\"\u00a0 1700 = n.340\/2.0,25\u00a0\"\"\u00a0 <\/b><\/span><\/span><\/span>n = 2,5.<\/b><\/span><\/span><\/span><\/p>\n

Assim, voc\u00ea ter\u00e1 3 n\u00f3s (um na extremidade fechada) e,<\/b><\/span><\/span><\/span> na <\/b><\/span><\/span><\/span>extremidade aberta<\/b><\/span><\/span><\/span>, em <\/b><\/span><\/span><\/span>cima dever\u00e1 ter um ventre.<\/b><\/span><\/span><\/span><\/p>\n

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

03- (UDESC-SC)\u00a0<\/b><\/span><\/span><\/span>Dois tubos sonoros <\/b><\/span><\/span><\/span>de um \u00f3rg\u00e3o t\u00eam o <\/b><\/span><\/span><\/span>mesmo comprimento<\/b><\/span><\/span><\/span>, <\/b><\/span><\/span><\/span>um deles <\/b><\/span><\/span><\/span>\u00e9 <\/b><\/span><\/span><\/span>aberto<\/b><\/span><\/span><\/span> e o <\/b><\/span><\/span><\/span>outro fechado. <\/b><\/span><\/span><\/span>O <\/b><\/span><\/span><\/span>tubo \u00a0fechado <\/b><\/span><\/span><\/span>emite o <\/b><\/span><\/span><\/span>som<\/b><\/span><\/span><\/span>\"\"<\/p>\n

fundamental de 500 Hz \u00e0 temperatura de 20<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sup><\/span>C e \u00e0 press\u00e3o atmosf\u00e9rica normal. <\/b><\/span><\/span><\/span><\/p>\n

Dentre<\/b><\/span><\/span><\/span> as <\/b><\/span><\/span><\/span>frequ\u00eancias abaixo, indique a<\/b><\/span><\/span><\/span> que esse tubo <\/b><\/span><\/span><\/span>n\u00e3o \u00e9 capaz de emitir.<\/b><\/span><\/span><\/span><\/p>\n

a)\u00a0<\/b><\/span><\/span><\/span>1500 Hz\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/b><\/span><\/span><\/span><\/p>\n

b)\u00a0<\/b><\/span><\/span><\/span>4500 Hz\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/b><\/span><\/span><\/span><\/p>\n

c)\u00a0<\/b><\/span><\/span><\/span>1000 Hz\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/b><\/span><\/span><\/span><\/p>\n

d) <\/b><\/span><\/span><\/span>2500 Hz\u00a0\u00a0\u00a0<\/b><\/span><\/span><\/span>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/b><\/span><\/span><\/span><\/p>\n

e)\u00a0<\/b><\/span><\/span><\/span>3500 Hz\u00a0\u00a0<\/b><\/span><\/span><\/span><\/p>\n

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

Os <\/b><\/span><\/span><\/span>tubos fechados s\u00f3 ressoam para harm\u00f4nicos \u00edmpares.<\/b><\/span><\/span><\/span><\/p>\n

Se a <\/b><\/span><\/span><\/span>frequ\u00eancia fundamental (n=1) \u00e9 500Hz, <\/b><\/span><\/span><\/span>ele <\/b><\/span><\/span><\/span>ressoar\u00e1 <\/b><\/span><\/span><\/span>para: <\/b><\/span><\/span><\/span>(n = 3 \"\" 3×500 = 1500 Hz)<\/b><\/span><\/span><\/span>, <\/b><\/span><\/span><\/span>(n = 5 \"\" 5×500 = 2500Hz)<\/b><\/span><\/span><\/span>, <\/b><\/span><\/span><\/span>(n = 7 \"\" 7×500 = 3500 Hz)<\/b><\/span><\/span><\/span>, <\/b><\/span><\/span><\/span>(n = 9 \"\" 9×500 = 4500 Hz)<\/b><\/span><\/span><\/span>, etc.\u00a0<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span><\/p>\n

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

04-(ITA-SP)<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

O <\/b><\/span><\/span><\/span>tubo mais curto <\/b><\/span><\/span><\/span>de um <\/b><\/span><\/span><\/span>\u00f3rg\u00e3o t\u00edpico de tubos tem um comprimento de aproximadamente 7 cm.<\/b><\/span><\/span><\/span> <\/b>Qual \u00e9 o<\/b><\/span><\/span><\/span><\/p>\n

harm\u00f4nico mais alto na faixa aud\u00edvel, <\/b><\/span><\/span><\/span>considerada como <\/b><\/span><\/span><\/span>estando entre 20 Hz e 20.000 Hz, <\/b><\/span><\/span><\/span>de um <\/b><\/span><\/span><\/span>tubo deste comprimento aberto nas duas extremidades?<\/b><\/span><\/span><\/span><\/p>\n

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

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

S\u00e3o <\/b><\/span><\/span><\/span>dados\u00a0 \"\"\u00a0\u00a0 L = 7 cm =<\/b><\/span><\/span><\/span> 0,07 m\u00a0 \"\"\u00a0\u00a0 <\/b><\/span><\/span><\/span>f<\/b><\/span><\/span><\/span>m\u00e1x<\/b><\/span><\/span><\/sub><\/span>\u00a0= <\/b><\/span><\/span><\/span>20.000 Hz\u00a0 \"\"\u00a0\u00a0 <\/b><\/span><\/span><\/span>f<\/b><\/span><\/span><\/span>m\u00edn<\/b><\/span><\/span><\/sub><\/span>\u00a0<\/b><\/span><\/span><\/span>= <\/b><\/span><\/span><\/span>20 Hz \"\" \u00a0<\/b><\/span><\/span><\/span>v<\/b><\/span><\/span><\/span>\u00a0= <\/b><\/span><\/span><\/span>340 m\/s.<\/b><\/span><\/span><\/span><\/p>\n

A <\/b><\/span><\/span><\/span>figura<\/b><\/span><\/span><\/span> mostra a <\/b><\/span><\/span><\/span>configura\u00e7\u00e3o <\/b><\/span><\/span><\/span>para o <\/b><\/span><\/span><\/span>primeiro harm\u00f4nico (n = 1) de um tubo aberto nas duas extremidades\u00a0 \"\" <\/b><\/span><\/span><\/span> o <\/b><\/span><\/span><\/span>comprimento do tubo (L) <\/b><\/span><\/span><\/span>\u00e9 <\/b><\/span><\/span><\/span>igual <\/b><\/span><\/span><\/span>a <\/b><\/span><\/span><\/span>meio comprimento de onda (<\/b><\/span><\/span><\/span>\u03bb<\/b><\/span><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>)\u00a0 \"\"<\/b><\/span><\/span><\/span>\u00a0\u00a0<\/b><\/span><\/span><\/span>\u03bb<\/b><\/span><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>\/2 = L \"\" <\/b><\/span><\/span><\/span>\u03bb<\/b><\/span><\/span><\/span><\/span>1 <\/b><\/span><\/span><\/sub><\/span>= 2L. Frequ\u00eancia <\/b><\/span><\/span><\/span>do <\/b><\/span><\/span><\/span>primeiro harm\u00f4nico\u00a0 \"\"<\/b><\/span><\/span><\/span>\u00a0 <\/b><\/span><\/span><\/span>V =\u00a0<\/b><\/span><\/span><\/span>\u03bb<\/b><\/span><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>.f<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>\u00a0 \"\"<\/b><\/span><\/span><\/span>\u00a0 340 = 2L.f<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>\u00a0 \"\"\u00a0 f<\/b><\/span><\/span><\/span>1 <\/b><\/span><\/span><\/sub><\/span>=340\/2.(0,07)\u00a0 \"\"\u00a0 <\/b><\/span><\/span><\/span>\"\"<\/p>\n

f<\/b><\/span><\/span><\/span>1 <\/b><\/span><\/span><\/sub><\/span>= 17.000\/7 Hz.\u00a0 <\/b><\/span><\/span><\/span><\/p>\n

Express\u00e3o da <\/b><\/span><\/span><\/span>frequ\u00eancia do n-\u00e9simo harm\u00f4nico<\/b><\/span><\/span><\/span>\u00a0 \"\"\u00a0 <\/b><\/span><\/span><\/span>f<\/b><\/span><\/span><\/span>n <\/b><\/span><\/span><\/sub><\/span>= nf<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>.<\/b><\/span><\/span><\/span><\/p>\n

Os <\/b><\/span><\/span><\/span>harm\u00f4nicos aud\u00edveis tem freq\u00fc\u00eancias menores que 20.000Hz\u00a0 \"\"<\/b><\/span><\/span><\/span>\u00a0 <\/b><\/span><\/span><\/span>f<\/b><\/span><\/span><\/span>n <\/b><\/span><\/span><\/sub><\/span>< 20.000\u00a0 \"\"<\/b><\/span><\/span><\/span>\u00a0 nf<\/b><\/span><\/span><\/span>1 <\/b><\/span><\/span><\/sub><\/span>< 20 000 \"\"<\/b><\/span><\/span><\/span><\/p>\n

n.(17.000)\/7 < 20.000\u00a0 \"\"\u00a0 n < 140\/17\u00a0 \"\"\u00a0 <\/b><\/span><\/span><\/span>n < 8,24 \u00a0(<\/b><\/span><\/span><\/span>\u00a0sendo <\/b><\/span><\/span><\/span>n<\/b><\/span><\/span><\/span> um <\/b><\/span><\/span><\/span>n\u00famero inteiro\u00a0\"\"<\/b><\/span><\/span><\/span>\u00a0 <\/b><\/span><\/span><\/span>n < 8).<\/b><\/span><\/span><\/span><\/p>\n

\u00a0Portanto os <\/b><\/span><\/span><\/span>sons aud\u00edveis est\u00e3o compreendidos entre o primeiro e o oitavo harm\u00f4nico <\/b><\/span><\/span><\/span>e o <\/b><\/span><\/span><\/span>som<\/b><\/span><\/span><\/span> <\/b>aud\u00edvel mais alto (maior frequ\u00eancia) \u00e9 o do oitavo harm\u00f4nico.<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span><\/p>\n

f<\/b><\/span><\/span><\/span>8 <\/b><\/span><\/span><\/sub><\/span>= 8f<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>\u00a0 \"\"<\/b><\/span><\/span><\/span>\u00a0 f<\/b><\/span><\/span><\/span>8<\/b><\/span><\/span><\/sub><\/span>=8.(17.000\/7)\u00a0 \"\"\u00a0<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>f<\/b><\/span><\/span><\/span>8 <\/b><\/span><\/span><\/sub><\/span>=19 428 Hz.<\/b><\/span><\/span><\/span><\/p>\n

 <\/p>\n

Confira os exerc\u00edcios com gabarito e resolu\u00e7\u00e3o comentada<\/span><\/a><\/h3>\n","protected":false},"excerpt":{"rendered":"

Tubos Sonoros C\u00e1lculo da velocidade de propaga\u00e7\u00e3o do som no ar Considere um diapas\u00e3o (fonte sonora) produzindo sons sobre a extremidade aberta de um tubo de vidro de comprimento L, sendo preenchido vagarosamente com \u00e1gua, o que conseguimos elevando o reservat\u00f3rio R de \u00e1gua, mantendo assim os n\u00edveis de R e do tubo aberto (figura abaixo) Quando o reservat\u00f3rio \u00e9<\/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-2345","page","type-page","status-publish","hentry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/2345","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=2345"}],"version-history":[{"count":2,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/2345\/revisions"}],"predecessor-version":[{"id":2355,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/2345\/revisions\/2355"}],"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=2345"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}