{"id":2381,"date":"2016-08-02T00:19:55","date_gmt":"2016-08-02T00:19:55","guid":{"rendered":"http:\/\/fisicaevestibular.com.br\/novo\/?page_id=2381"},"modified":"2024-08-23T14:50:43","modified_gmt":"2024-08-23T14:50:43","slug":"resolucao-comentada-dos-exercicios-de-vestibulares-sobre-ondas-estacionarias","status":"publish","type":"page","link":"https:\/\/fisicaevestibular.com.br\/novo\/ondulatoria\/acustica\/ondas-estacionarias\/resolucao-comentada-dos-exercicios-de-vestibulares-sobre-ondas-estacionarias\/","title":{"rendered":"Ondas Estacion\u00e1rias – Resolu\u00e7\u00e3o"},"content":{"rendered":"

Resolu\u00e7\u00e3o comentada dos exerc\u00edcios de vestibulares sobre <\/b><\/span><\/span><\/span><\/p>\n

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

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

01-<\/b><\/span><\/span><\/span><\/span> 4<\/b><\/span><\/span><\/span><\/span>\u03bb<\/b><\/span><\/span><\/span>\/2=1\u00a0 —\u00a0\u00a0<\/b><\/span><\/span><\/span><\/span>\u03bb<\/b><\/span><\/span><\/span>=1\/2m\u00a0 —\u00a0 V=<\/b><\/span><\/span><\/span><\/span>\u03bb<\/b><\/span><\/span><\/span>f\u00a0 —\u00a0 V=1\/2.1000\u00a0 —\u00a0\u00a0V=500m\/s.<\/b><\/span><\/span><\/span><\/span><\/p>\n

02-<\/b><\/span><\/span><\/span> Formam-se ondas estacion\u00e1rias com os pedacinhos de papel jogados pelos ventres formados <\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

nos pontos D, F e H. figura acima<\/b><\/span><\/span><\/span><\/p>\n

03-<\/b><\/span><\/span><\/span> 4<\/b><\/span><\/span><\/span>\u03bb<\/b><\/span><\/span><\/span><\/span>\/2=60\u00a0 —\u00a0\u00a0<\/b><\/span><\/span><\/span>\u03bb<\/b><\/span><\/span><\/span><\/span>=30cm\u00a0 —\u00a0 V=<\/b><\/span><\/span><\/span>\u03bb<\/b><\/span><\/span><\/span><\/span>f\u00a0 —\u00a0 V=30.60\u00a0 —\u00a0V=1800cm\/s=18m\/s<\/b><\/span><\/span><\/span><\/p>\n

04-<\/b><\/span><\/span><\/span><\/p>\n

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

\"\"<\/p>\n

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

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

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

(16) Correta.\u00a0 V=\"\"\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>=(\u221a(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 F= 112,995N<\/b><\/span><\/span><\/span><\/p>\n

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

05-<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span><\/span>Na configura\u00e7\u00e3o da figura abaixo, onde L \u00e9 o comprimento da corda, a frequ\u00eancia \u00e9 de 360Hz.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Sendo\u00a0l<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>\u00a0o comprimento de onda dessa onda estacion\u00e1ria, temos que 3l<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>\/2=L\u00a0 —\u00a0\u00a0l<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>=2L\/3\u00a0 — V<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>=l<\/b><\/span><\/span><\/span>1.<\/b><\/span><\/span><\/sub><\/span>f<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>\u00a0 —\u00a0 V<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>=2L\/3.360\u00a0 —\u00a0 V<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>=240L<\/b><\/span><\/span><\/span><\/p>\n

Como a velocidade V na corda \u00e9 a mesma (mesmo meio) e V=\u03bbf,\u00a0\u03bb\u00a0e f s\u00e3o inversamente proporcionais. Assim, sendo L o mesmo, se aumentarmos f,\u00a0\u03bb<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/sub><\/span>ir\u00e1 diminuir e teremos um ventre a mais na corda.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

4\u03bb<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span>\/2=L\u00a0 —\u00a0\u00a0\u03bb<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span>=L\/2\u00a0 —\u00a0 V<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span>=\u03bb<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span>.f\u00a0 —\u00a0 V<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>=V<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span>\u00a0(mesmo meio)\u00a0 —\u00a0 240L=L\/2f<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span>\u00a0 —\u00a0f<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span>=480Hz<\/b><\/span><\/span><\/span><\/p>\n

\u00a0R- C<\/b><\/span><\/span><\/span><\/p>\n

06-<\/b><\/span><\/span><\/span> a)\u00a0\u03bb\/2=12\u00a0 —\u00a0\u00a0\u03bb=24cm = 0,24m\u00a0<\/b><\/span><\/span><\/span><\/p>\n

b) F=P=mg\u00a0 —\u00a0 F=0,18.10\u00a0 —\u00a0 F=1,8N\u00a0 —\u00a0\u00a0\u00a0\u00a0m=5.10\u20114\u2011kg\/m\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/b><\/span><\/span><\/span><\/p>\n

\u00a0V=\u221a(F\/\u03bc)\u00a0 —\u00a0 V=\u221a(1,8\/5.10<\/b><\/span><\/span><\/span>-4<\/b><\/span><\/span><\/sup><\/span>)\u00a0 —\u00a0 V=\u221a(36.10<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>)\u00a0 = 60m\/sm\u00a0 —\u00a0 V=\u03bbf\u00a0 —\u00a0 60=0,24f\u00a0 —\u00a0f=250Hz<\/b><\/span><\/span><\/span><\/p>\n

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

07-<\/b><\/span><\/span><\/span> 3\u03bb\/2=15\u00a0 —\u00a0\u00a0\u03bb=10m\u00a0 —\u00a0 esse intervalo de tempo 0,50s \u00e9 metade do per\u00edodo de cada uma das ondas que geraram a onda estacion\u00e1ria\u00a0 —\u00a0 T\/2=0,50\u00a0 —\u00a0 T=1s\u00a0 —\u00a0 f=1\/T\u00a0 —\u00a0 f=1\/1\u00a0 —\u00a0 f=1Hz\u00a0 —\u00a0 V=\u03bbf\u00a0 —\u00a0 V= 10.1\u00a0 —\u00a0\u00a0V=10m\/s<\/b><\/span><\/span><\/span><\/p>\n

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

O8-<\/b><\/span><\/span><\/span> 3\u03bb\/2=0,9 \u00a0—\u00a0\u00a0\u03bb=0,6m<\/b><\/span><\/span><\/span><\/p>\n

\u03bc=m\/L\u00a0 —\u00a0\u00a0m=0,01kg\/m\u00a0 —\u00a0 V=\u221a(F\/<\/b><\/span><\/span><\/span>\u03bc<\/b><\/span><\/span><\/span><\/span>)\u00a0 —\u00a0 V=\u221a(900\/0,01)\u00a0 —\u00a0 V=300m\/s\u00a0 —\u00a0 V=<\/b><\/span><\/span><\/span>\u03bb<\/b><\/span><\/span><\/span><\/span>f\u00a0 —\u00a0 300=0,6.f\u00a0 —\u00a0 f=500Hz<\/b><\/span><\/span><\/span><\/p>\n

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

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

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

12-<\/b><\/span><\/span><\/span>\u00a0Da equa\u00e7\u00e3o fundamental da ondulat\u00f3ria\u00a0 —\u00a0 r\u00e1dio da cidade\u00a0 —\u00a0 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 —\u00a0 r\u00e1dio pirata\u00a0 —\u00a0 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 —\u00a0 como a velocidade de propaga\u00e7\u00e3o da onda \u00e9 a mesma, pois se trata do mesmo meio (ar), se as frequ\u00eancias s\u00e3o iguais, os comprimentos onde tamb\u00e9m o ser\u00e3o\u00a0 —\u00a0\u00a0R- E<\/b><\/span><\/span><\/span><\/p>\n

13-<\/b><\/span><\/span><\/span><\/span>\u00a0Observe a figura abaixo:<\/b><\/span><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Ventres\u00a0 —\u00a0 50\/0,5=100\u00a0 —\u00a0 comprimento de onda\u00a0 —\u00a0\u00a0<\/b><\/span><\/span><\/span>\u03bb<\/b><\/span><\/span><\/span><\/span>=1m\u00a0 —\u00a0\u00a0R- D<\/b><\/span><\/span><\/span><\/p>\n

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

14-<\/b><\/span><\/span><\/span>\u00a0Ondas estacion\u00e1rias\u00a0s\u00e3o ondas formadas pela superposi\u00e7\u00e3o de duas ondas id\u00eanticas, de mesma amplitude, mesma freq\u00fc\u00eancia, mesmo comprimento de onda e que se movem na mesma dire\u00e7\u00e3o e sentidos opostos<\/b><\/span><\/span><\/span><\/p>\n

* Os pontos A, C, E, G e I s\u00e3o n\u00f3s ou nodos e n\u00e3o se movem, s\u00e3o fixos.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Todos os pontos que est\u00e3o entre AC, CE, EG e GI s\u00e3o ventres (fusos) e est\u00e3o sempre em movimento vibrat\u00f3rio.<\/b><\/span><\/span><\/span><\/p>\n

A dist\u00e2ncia entre dois n\u00f3s consecutivos \u00e9 sempre\u00a0\u03bb\/2.<\/b><\/span><\/span><\/span><\/p>\n

Observe na figura do exerc\u00edcio que \u03bb\/2=6m\u00a0 —\u00a0 \u03bb\/2=6\u00a0 —\u00a0\u00a0\u03bb=12m.<\/b><\/span><\/span><\/span><\/p>\n

15-<\/b><\/span><\/span><\/span> \u00a0O ponto 2 da corda \u00e9 um n\u00f3 (ou nodo) da onda estacion\u00e1ria e permanece fixo\u00a0 —\u00a0 os pontos 1 e 3 possuem velocidade nula nas extremidades superiores e inferiores e velocidades m\u00e1ximas quando passam pela centro (onde est\u00e3o esses pontos),\u00a0 apenas que eles possuem velocidades de sentidos contr\u00e1rios, ou seja, enquanto um est\u00e1 subindo o outro estar\u00e1 descendo\u00a0 —\u00a0\u00a0R-\u00a0 D.<\/b><\/span><\/span><\/span><\/p>\n

Se voc\u00ea quer entender como se originam ondas estacion\u00e1rias leia atentamente a teoria abaixo:<\/b><\/span><\/span><\/span><\/p>\n

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.<\/b><\/span><\/span><\/span><\/p>\n

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

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

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

No instante t=0, as 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

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

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

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

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

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

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

\u00a0Observe que, em todos os instantes, os pontos P, Q e R, da onda resultante n\u00e3o se moveram. Esses pontos, sempre fixos s\u00e3o chamados de\u00a0nodos ou n\u00f3s\u00a0e est\u00e3o em interfer\u00eancia destrutiva\u00a0 —\u00a0 suas velocidades verticais s\u00e3o nulas.<\/b><\/span><\/span><\/span><\/p>\n

Observe tamb\u00e9m que, em todos os instantes, todos os pontos compreendidos entre P e Q e entre Q e R, est\u00e3o em constante\u00a0 movimento, subindo e descendo, em interfer\u00eancia construtiva, e sua amplitude ser\u00e1 a soma das amplitudes das ondas constituintes. Esses pontos s\u00e3o chamados de\u00a0ventres..<\/b><\/span><\/span><\/span><\/p>\n

Observe na figura abaixo, que os pontos A, C, E, G e I s\u00e3o n\u00f3s e que os pontos B, D, F e H s\u00e3o ventres.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Se o comprimento de onda de cada onda que originou a estacion\u00e1ria \u00e9\u00a0l, a dist\u00e2ncia entre dois n\u00f3s consecutivos (fuso) vale\u00a0l\/2.<\/b><\/span><\/span><\/span><\/p>\n

Entre os n\u00f3s, os pontos dos ventres vibram na vertical com a mesma freq\u00fc\u00eancia que \u00e9 a mesma de cada onda que se superp\u00f5e, mas com amplitudes diferentes (figura abaixo)<\/b><\/span><\/span><\/span><\/p>\n

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

Como a freq\u00fc\u00eancia de cada ponto \u00e9 a mesma, o per\u00edodo (tempo que cada ponto demora para efetuar um \u201csobe e desce\u201d completo) tamb\u00e9m ser\u00e1. Assim, a\u00a0velocidade vertical\u00a0do ponto A \u00e9 maior que a do ponto A<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>, que por sua vez, \u00e9 maior que a do ponto A<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span>.<\/b><\/span><\/span><\/span><\/p>\n

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

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

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

16-<\/b><\/span><\/span><\/span> \u00a0Equa\u00e7\u00f5es das ondas estacion\u00e1rias em uma corda de extremidades fixas\u00a0 —\u00a0 f<\/b><\/span><\/span><\/span>n<\/b><\/span><\/span><\/sub><\/span>=n.V\/2.L\u00a0 —\u00a0 V=\u221a(T\/\u03bc)\u00a0 —\u00a0 f \u2013 frequ\u00eancia do harm\u00f4nico (que \u00e9 sempre a mesma que a da fonte)\u00a0 —\u00a0 n \u2013 ordem do harm\u00f4nico\u00a0 —\u00a0 V \u2013 velocidade de propaga\u00e7\u00e3o da onda na corda\u00a0 —\u00a0 L \u2013 comprimento da corda\u00a0 —\u00a0 T \u2013 for\u00e7a que traciona a corda\u00a0 —\u00a0 \u03bc \u2013 densidade linear da corda\u00a0 —\u00a0 na situa\u00e7\u00e3o da<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

figura 1\u00a0 —\u00a0 as for\u00e7as que agem sobre o corpo s\u00e3o seu peso\u00a0\"\"\u00a0e a for\u00e7a de tra\u00e7\u00e3o no fio\u00a0\"\"\u00a0\u00a0—\u00a0 no equil\u00edbrio P e T se anulam\u00a0 —\u00a0 P=T\u00a0 —\u00a0 P=mg=\u03c1Vg\u00a0 —\u00a0 T= \u03c1Vg\u00a0 —\u00a0 observe pela figura 1 que a configura\u00e7\u00e3o fornecida corresponde ao 2<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sup><\/span>\u00a0harm\u00f4nico (n=2)\u00a0 —\u00a0 f<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span>=2.V\/2L=2.\u221a(T\/\u03bc)\/2L\u00a0 —\u00a0 f<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span>=1\/L.\u221a (\u03c1Vg\/\u03bc)\u00a0 —\u00a0 na situa\u00e7\u00e3o da figura 2 surge sobre o corpo tamb\u00e9m um empuxo\u00a0\"\", vertical e<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

para cima e no equil\u00edbrio\u00a0 —\u00a0 P= T\u2019 + E\u00a0 —\u00a0 T\u2019= P \u2013 E\u00a0 —\u00a0 T\u2019 = \u03c1Vg \u2013 \u03b4Vg\u00a0 —\u00a0 T\u2019=Vg(\u03c1 \u2013 \u03b4)\u00a0 —\u00a0 observe pela figura 2 que a configura\u00e7\u00e3o fornecida corresponde ao 4<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sup><\/span>\u00a0harm\u00f4nico (n=4)\u00a0 —<\/b><\/span><\/span><\/span><\/p>\n

f<\/b><\/span><\/span><\/span>4<\/b><\/span><\/span><\/sub><\/span>=4V\u2019\/2L\u00a0 —\u00a0 V\u2019=\u221a(T\u2019\/\u03bc)= \u221a( Vg(\u03c1 \u2013 \u03b4)\/\u03bc)\u00a0 —\u00a0 f<\/b><\/span><\/span><\/span>4<\/b><\/span><\/span><\/sub><\/span>=4.\u221a( Vg(\u03c1 \u2013 \u03b4)\/\u03bc)\/2L\u00a0 —\u00a0 f<\/b><\/span><\/span><\/span>4<\/b><\/span><\/span><\/sub><\/span>=(2\/L).\u221a( Vg(\u03c1 \u2013 \u03b4)\/\u03bc)\u00a0 —\u00a0 observe que nos dois casos a frequ\u00eancia de oscila\u00e7\u00e3o \u00e9 a mesma, que \u00e9 a da fonte\u00a0 —\u00a0 f<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span>=f<\/b><\/span><\/span><\/span>4<\/b><\/span><\/span><\/sub><\/span>\u00a0 — 1\/L.\u221a (\u03c1Vg\/\u03bc) = (2\/L).\u221a( Vg(\u03c1 \u2013 \u03b4)\/\u03bc)\u00a0 —\u00a0 1\/L.\u221a (\u03c1Vg\/\u03bc) = 1\/L.\u221a(4 Vg(\u03c1 \u2013 \u03b4)\/\u03bc)\u00a0 —\u00a0 \u03c1 = 4(\u03c1 \u2013 \u03b4)\u00a0 —\u00a0 \u03c1 = 4\u03c1 \u2013 4 \u03b4\u00a0 —\u00a03\u03c1 = 4 \u03b4\u00a0 —\u00a0\u00a0 \u03c1\/\u03b4 = 4\/3\u00a0 —\u00a0\u00a0R- B<\/b><\/span><\/span><\/span><\/p>\n

17-<\/b><\/span><\/span><\/span> Observe nas figuras abaixo as ondas estacion\u00e1rias formadas em cada caso\u00a0 —\u00a0 \u03b3<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>\/2=L\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 V<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>=2L.f<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span><\/p>\n

\"\"<\/p>\n

(I)\u00a0 —\u03b3<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span>\/2=L\/2 —\u00a0 \u03b3<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span>=L\u00a0 —\u00a0 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 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)\u00a0 —\u00a0 como a velocidade de propaga\u00e7\u00e3o em cada caso \u00e9 a mesma\u00a0 —\u00a0 V<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>=V<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span>\u00a0 —\u00a0 I=II\u00a0 —\u00a0 2Lf<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>=L<\/b><\/span><\/span><\/span>f<\/b><\/span><\/span><\/sub><\/span>2\u00a0 —\u00a0 2.220=f<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span>\u00a0 —\u00a0 f<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span>=440Hz\u00a0 —\u00a0\u00a0R- A<\/b><\/span><\/span><\/span><\/p>\n

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

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

Resolu\u00e7\u00e3o comentada dos exerc\u00edcios de vestibulares sobre Ondas Estacion\u00e1rias \u00a0 01- 4\u03bb\/2=1\u00a0 —\u00a0\u00a0\u03bb=1\/2m\u00a0 —\u00a0 V=\u03bbf\u00a0 —\u00a0 V=1\/2.1000\u00a0 —\u00a0\u00a0V=500m\/s. 02- Formam-se ondas estacion\u00e1rias com os pedacinhos de papel jogados pelos ventres formados nos pontos D, F e H. figura acima 03- 4\u03bb\/2=60\u00a0 —\u00a0\u00a0\u03bb=30cm\u00a0 —\u00a0 V=\u03bbf\u00a0 —\u00a0 V=30.60\u00a0 —\u00a0V=1800cm\/s=18m\/s 04- (01) Errada. O movimento de cada ponto da onda estacion\u00e1ria \u00e9 somente<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":2377,"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-2381","page","type-page","status-publish","hentry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/2381","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=2381"}],"version-history":[{"count":3,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/2381\/revisions"}],"predecessor-version":[{"id":10904,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/2381\/revisions\/10904"}],"up":[{"embeddable":true,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/2377"}],"wp:attachment":[{"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/media?parent=2381"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}