{"id":2390,"date":"2016-08-02T00:39:33","date_gmt":"2016-08-02T00:39:33","guid":{"rendered":"http:\/\/fisicaevestibular.com.br\/novo\/?page_id=2390"},"modified":"2024-08-23T14:43:06","modified_gmt":"2024-08-23T14:43:06","slug":"resolucao-comentada-dos-exercicios-de-vestibulares-sobre-cordas-vibrantes-harmonicos","status":"publish","type":"page","link":"https:\/\/fisicaevestibular.com.br\/novo\/ondulatoria\/acustica\/cordas-vibrantes\/resolucao-comentada-dos-exercicios-de-vestibulares-sobre-cordas-vibrantes-harmonicos\/","title":{"rendered":"Cordas vibrantes – Harm\u00f4nicos – Resolu\u00e7\u00e3o"},"content":{"rendered":"

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

Cordas vibrantes – Harm\u00f4nicos<\/b><\/span><\/span><\/span><\/p>\n

01-<\/b><\/span><\/span><\/span> <\/b>75 oscila\u00e7\u00f5es \u2013 30s\u00a0 —\u00a0 1 oscila\u00e7\u00e3o\u00a0 —\u00a0 T=30\/75s\u00a0 —\u00a0 f=1\/T\u00a0 —\u00a0 f=75\/30\u00a0 —\u00a0 f=2,5Hz — f<\/b><\/span><\/span><\/span>n<\/b><\/span><\/span><\/sub><\/span>=nf<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>\u00a0 — supondo n=1\u00a0 —\u00a0 f<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>=2,5Hz\u00a0 —\u00a0 a pr\u00f3xima ocorre quando n=2\u00a0 —\u00a0 f<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span>=2f<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>\u00a0 —\u00a0 f<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span>=2.2,5\u00a0 —\u00a0\u00a0<\/b><\/span><\/span><\/span>f<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span>=5Hz<\/b><\/span><\/span><\/span>\u00a0\u00a0\u00a0 R- D<\/b><\/span><\/span><\/span><\/p>\n

02-<\/b><\/span><\/span><\/span> <\/b>L=0,6m\u00a0 —\u00a0 som fundamental (1 fuso)\u00a0 — n=1\u00a0 —\u00a0 f<\/b><\/span><\/span><\/span>n<\/b><\/span><\/span><\/sub><\/span>=nV\/2L\u00a0 —\u00a0 f<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>=V\/2L\u00a0 —\u00a0 220=V\/2.0,6\u00a0 —\u00a0\u00a0<\/b><\/span><\/span><\/span>V=264m\/s<\/b><\/span><\/span><\/span>\u00a0\u00a0\u00a0 R- D<\/b><\/span><\/span><\/span><\/p>\n

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

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

b) P=mg\u00a0 —\u00a0 P=0,18.10\u00a0 —\u00a0 P=1,8N\u00a0 —\u00a0<\/b><\/span><\/span><\/span> <\/b>v = \"\"<\/b><\/span><\/span><\/span>\u00a0 <\/b><\/span><\/span><\/span>—\u00a0<\/b><\/span><\/span>v = \"\"<\/b><\/span><\/span>\u00a0 —\u00a0 V=\"\"\u00a0 —\u00a0 V=60m\/s<\/b><\/span><\/span><\/span><\/p>\n

V= \u03bbf\u00a0 —\u00a0 60=0,24f\u00a0 —\u00a0\u00a0<\/b><\/span><\/span><\/span>f=250Hz<\/b><\/span><\/span><\/span><\/p>\n

04-<\/b><\/span><\/span><\/span> <\/b>Os tr\u00eas maiores comprimentos de onda s\u00e3o os 3 primeiros<\/b><\/span><\/span><\/span><\/p>\n

1<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sup><\/span>\u00a0–\u00a0\u03bb<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>\/2=90\u00a0 —\u00a0\u00a0\u03bb<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>=180cm\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 2<\/b><\/span><\/span><\/span>0<\/b><\/span><\/span><\/sup><\/span>\u00a0-2\u03bb<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span>\/2=90\u00a0 —\u00a0\u03bb<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span>=90cm\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 3<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sup><\/span>\u00a0– 3\u03bb<\/b><\/span><\/span><\/span>3<\/b><\/span><\/span><\/sub><\/span>\/2=90\u00a0 —\u00a0\u00a0\u03bb<\/b><\/span><\/span><\/span>3<\/b><\/span><\/span><\/sub><\/span>=60cm<\/b><\/span><\/span><\/span><\/p>\n

05- Som fundamental\u00a0 —\u00a0 n=1\u00a0 —\u00a0 f<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>=1\/2.0,5\"\"\u00a0 —\u00a0 200=1\/2.0,5\"\"\u00a0 —\u00a0 4.10<\/b><\/span><\/span><\/span>4<\/b><\/span><\/span><\/sup><\/span>=T\/10<\/b><\/span><\/span><\/span>-3<\/b><\/span><\/span><\/sup><\/span>\u00a0 —\u00a0 T=40N=P<\/b><\/span><\/span><\/span><\/p>\n

P=mg\u00a0 —\u00a0 40=m10\u00a0 —\u00a0\u00a0<\/b><\/span><\/span><\/span>m=4kg\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/b><\/span><\/span><\/span>R- B<\/b><\/span><\/span><\/span><\/p>\n

06-<\/b><\/span><\/span><\/span>\u03bb<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>\/2=50\u00a0 —\u00a0\u00a0<\/b><\/span><\/span><\/span>\u03bb<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>=100cm\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/b><\/span><\/span><\/span>R- D<\/b><\/span><\/span><\/span><\/p>\n

07-<\/b><\/span><\/span><\/span> <\/b>a)\u00a0\u03bb\u00a0= 2.35 = 70 cm<\/b><\/span><\/span><\/span><\/p>\n

f = 680 Hz<\/b><\/span><\/span><\/span><\/p>\n

v =\u00a0\u00a0\u03bb.f = 0,7.680 =\u00a0<\/b><\/span><\/span><\/span>476 m\/s<\/b><\/span><\/span><\/span><\/p>\n

b) v =\u00a0\u00a0\u03bb.f<\/b><\/span><\/span><\/span><\/p>\n

340 =\u00a0l680<\/b><\/span><\/span><\/span><\/p>\n

\u03bb\u00a0= 340\/680 = 0,5 m =\u00a0<\/b><\/span><\/span><\/span>50 cm<\/b><\/span><\/span><\/span><\/p>\n

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

08-<\/b><\/span><\/span><\/span> <\/b>f<\/b><\/span><\/span><\/span>n<\/b><\/span><\/span><\/sub><\/span>=840Hz\u00a0 —\u00a0 f<\/b><\/span><\/span><\/span>n+1<\/b><\/span><\/span><\/sub><\/span>=1260Hz\u00a0 —\u00a0 f<\/b><\/span><\/span><\/span>n+1<\/b><\/span><\/span><\/sub><\/span>-f<\/b><\/span><\/span><\/span>n<\/b><\/span><\/span><\/sub><\/span>=1260-840=nV\/2L\u00a0 —\u00a0 210=1.210\/2L\u00a0 —\u00a0<\/b><\/span><\/span><\/span>L=0,5m=50cm<\/b><\/span><\/span><\/span><\/p>\n

09-<\/b><\/span><\/span><\/span> <\/b>Quando tocada na regi\u00e3o da boca, comprimento \u00e9 L e f=440Hz\u00a0 —\u00a0 V=\u03bb<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>f<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>\u00a0 —\u00a0 freq\u00fc\u00eancia fundamental \u2013 1<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sup><\/span>\u00a0harm\u00f4nico \u2013<\/b><\/span><\/span><\/span>\"\"<\/p>\n

\u00a0\u03bb<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>\/2=L\u00a0 —\u00a0\u00a0\u03bb<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>=2L\u00a0 —\u00a0 V=2L.440\u00a0 —\u00a0 V=880L<\/b><\/span><\/span><\/span><\/p>\n

Quando tocada na regi\u00e3o da boca, quando o comprimento for L\/3 a freq\u00fc\u00eancia fundamental ser\u00e1\u00a0 —\u00a0\u03bb<\/b><\/span><\/span><\/span>x<\/b><\/span><\/span><\/sub><\/span>\/2=2L\/3\u00a0 —\u00a0\u03bb<\/b><\/span><\/span><\/span>x<\/b><\/span><\/span><\/sub><\/span>=4L\/3<\/b><\/span><\/span><\/span><\/p>\n

V=\u03bb<\/b><\/span><\/span><\/span>x<\/b><\/span><\/span><\/sub><\/span>.f<\/b><\/span><\/span><\/span>x<\/b><\/span><\/span><\/sub><\/span>\u00a0 —\u00a0 V=4L\/3.f<\/b><\/span><\/span><\/span>x<\/b><\/span><\/span><\/sub><\/span>\u00a0 —\u00a0 880L=4L\/3. f<\/b><\/span><\/span><\/span>x<\/b><\/span><\/span><\/sub><\/span>\u00a0 —\u00a0\u00a0<\/b><\/span><\/span><\/span>f<\/b><\/span><\/span><\/span>x<\/b><\/span><\/span><\/sub><\/span>=660Hz<\/b><\/span><\/span><\/span><\/p>\n

10-<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>\u00b5=10g\/m=0,01kg\/m<\/b><\/span><\/span><\/span><\/p>\n

Adjacentes\u00a0 —\u00a0 uma \u00e9 n e a seguinte n+1<\/b><\/span><\/span><\/span><\/p>\n

f<\/b><\/span><\/span><\/span>n<\/b><\/span><\/span><\/sub><\/span>=n\/2L<\/b><\/span><\/span><\/span>.\"\"<\/b><\/span><\/span><\/span>\u00a0 —\u00a0 f<\/b><\/span><\/span><\/span>n+1<\/b><\/span><\/span><\/sub><\/span>=(n+1)\/2L<\/b><\/span><\/span><\/span>.\"\"<\/b><\/span><\/span><\/span>\u00a0\u00a0\u00a0 —\u00a0 f<\/b><\/span><\/span><\/span>n<\/b><\/span><\/span><\/sub><\/span>\u00a0\u2013 f<\/b><\/span><\/span><\/span>n+1<\/b><\/span><\/span><\/sub><\/span>=1\/2L<\/b><\/span><\/span><\/span>.\"\"<\/b><\/span><\/span><\/span>\u00a0\u00a0 —\u00a0 (125-100)=1\/2.2\"\"\u00a0\u00a0 (125-100)=1\/2.2 \"\"\u00a0\u00a0 \u00a0—\u00a0 (100)<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>=(T\/0,01)<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>\u00a0 —\u00a0 10<\/b><\/span><\/span><\/span>4<\/b><\/span><\/span><\/sup><\/span>=T\/10<\/b><\/span><\/span><\/span>-2<\/b><\/span><\/span><\/sup><\/span> — T=100N=P\u00a0 — P=mg\u00a0 —\u00a0 100=m10\u00a0 —\u00a0\u00a0<\/b><\/span><\/span><\/span>m=10kg<\/b><\/span><\/span><\/span>\u00a0\u00a0\u00a0 R- A\u00a0<\/b><\/span><\/span><\/span><\/p>\n

11-<\/b><\/span><\/span><\/span> <\/b>a) RESSON\u00c2NCIA<\/b><\/span><\/span><\/span><\/p>\n

b) I – Todo corpo tem suas freq\u00fc\u00eancias naturais de vibra\u00e7\u00e3o (modos de vibra\u00e7\u00e3o).<\/b><\/span><\/span><\/span><\/p>\n

II – Quando o corpo \u00e9 submetido a est\u00edmulos externos peri\u00f3dicos com freq\u00fc\u00eancia igual a uma de suas freq\u00fc\u00eancias naturais, o corpo oscilar\u00e1 com maior amplitude, quando se diz que o mesmo est\u00e1 em resson\u00e2ncia.<\/b><\/span><\/span><\/span><\/p>\n

III – No caso, Flavita ajustava a tens\u00e3o na corda 4 para deix\u00e1-la com as mesmas freq\u00fc\u00eancias naturais das da corda 5, pressionada entre o 4<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sup><\/span>\u00a0e o 5<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sup><\/span>\u00a0traste.<\/b><\/span><\/span><\/span><\/p>\n

12-<\/b><\/span><\/span><\/span> \u00a0<\/b><\/span><\/span><\/span>A fonte \u00e9 a mesma (mesma f)—A tra\u00e7\u00e3o \u00e9 a mesma (mesmo peso \u2013 P\/2) — L \u00e9 o mesmo (dist\u00e2ncia entre fonte e roldanas iguais)<\/b><\/span><\/span><\/span><\/p>\n

A corda com tr\u00eas fusos \u00e9 a mais densa (m<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>), pois como T \u00e9 a mesma (v =\"\"\u00a0) V e\u00a0m\u00a0s\u00e3o inversamente proporcionais e V \u00e9 menor na mais densa. Da equa\u00e7\u00e3o V=\u03bbf, como f \u00e9 a mesma, menor V implica em menor\u00a0l, que \u00e9 o da corda com tr\u00eas fusos (m<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>).<\/b><\/span><\/span><\/span><\/p>\n

Fio 1\u00a0 —\u00a0 3<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sup><\/span>\u00a0harm\u00f4nico\u00a0 —\u00a0 n=3\u00a0 —\u00a0 f<\/b><\/span><\/span><\/span>n<\/b><\/span><\/span><\/sub><\/span>=nV\/2L\"\"\u00a0 —\u00a0 f<\/b><\/span><\/span><\/span>3<\/b><\/span><\/span><\/sub><\/span>=3V\/2L\"\"<\/b><\/span><\/span><\/span><\/p>\n

Fio 2\u00a0 —\u00a0 1<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sup><\/span>\u00a0haem\u00f4nico\u00a0 —\u00a0 n=1\u00a0 —\u00a0 f<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>=1V\/2L\"\"\u00a0<\/b><\/span><\/span><\/span><\/p>\n

f<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>=f<\/b><\/span><\/span><\/span>3<\/b><\/span><\/span><\/sub><\/span>=f\u00a0 —\u00a0 1V\/2L.\"\"\u00a0= 3V\/2L\"\" \u00a0 —\u00a0\u00a0\"\"\u00a0= 3\"\"\u00a0 —\u00a0 (\"\")<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>\u00a0= (3\"\")<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>\u00a0 —\u00a0\u00a0\u00b5<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>=\u00b5\/9\u00a0\u00a0<\/b><\/span><\/span><\/span><\/p>\n

13-<\/b><\/span><\/span><\/span> <\/b>Sendo V inversamente proporcional a\u00a0m\u00a0 —\u00a0 V<\/b><\/span><\/span><\/span>A<\/b><\/span><\/span><\/sub><\/span>>V<\/b><\/span><\/span><\/span>B<\/b><\/span><\/span><\/sub><\/span>. Como o comprimento de onda \u00e9 o mesmo, de V=\u03bbf, conclu\u00edmos que V \u00e9 diretamente proporcional a f, ou seja, f<\/b><\/span><\/span><\/span>A\u00a0<\/b><\/span><\/span><\/sub><\/span>><\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/sub><\/span>f<\/b><\/span><\/span><\/span>B<\/b><\/span><\/span><\/sub><\/span>.\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 R- C<\/b><\/span><\/span><\/span><\/p>\n

14-<\/b><\/span><\/span><\/span> <\/b>O Sol considerado \u00e9\u00a0 a frequ\u00eancia fundamental\u00a0 —\u00a0\u00a0\u03bb<\/b><\/span><\/span><\/span>Sol<\/b><\/span><\/span><\/sub><\/span>\/2=0,64\u00a0 —\u00a0\u00a0\u03bb<\/b><\/span><\/span><\/span>Sol<\/b><\/span><\/span><\/sub><\/span>=1,28m\u00a0 —\u00a0 V=\u03bb<\/b><\/span><\/span><\/span>Sol<\/b><\/span><\/span><\/sub><\/span>f<\/b><\/span><\/span><\/span>Sol<\/b><\/span><\/span><\/sub><\/span>=392.1,28=501,76m\/s<\/b><\/span><\/span><\/span><\/p>\n

Como a corda \u00e9 a mesma (mesmo meio), a velocidade V \u00e9 a mesma para a freq\u00fc\u00eancia L\u00e1, tamb\u00e9m fundamental\u00a0 —<\/b><\/span><\/span><\/span><\/p>\n

V=\u03bb<\/b><\/span><\/span><\/span>L\u00e1<\/b><\/span><\/span><\/sub><\/span>.f<\/b><\/span><\/span><\/span>L\u00e1\u00a0<\/b><\/span><\/span><\/sub><\/span>\u00a0—\u00a0 501,76=\u03bb<\/b><\/span><\/span><\/span>L\u00e1<\/b><\/span><\/span><\/sub><\/span>.440\u00a0 —\u00a0\u03bb<\/b><\/span><\/span><\/span>L\u00e1<\/b><\/span><\/span><\/sub><\/span>=1,14m\u00a0 —\u00a0 som fundamental\u00a0 —\u00a0\u00a0\u03bb<\/b><\/span><\/span><\/span>L\u00e1<\/b><\/span><\/span><\/sub><\/span>\/2=L\u00a0 —\u00a0 1,14\/2=L\u00a0 —\u00a0\u00a0<\/b><\/span><\/span><\/span>L=0,57m<\/b><\/span><\/span><\/span><\/p>\n

15-<\/b><\/span><\/span><\/span> <\/b>Se o comprimento da corda \u00e9 igual a meio comprimento de onda, trata-se da freq\u00fc\u00eancia fundamental e\u00a0\u03bb\/2=1\u00a0 —\u00a0\u00a0\u00a0\u03bb\/=2m<\/b><\/span><\/span><\/span><\/p>\n

V=\u00a0\u03bb.f\u00a0 —\u00a0 V=2.260\u00a0 —\u00a0 V=520m\/s\u00a0 —\u00a0 V=\"\",\u00a0 —\u00a0 520=\"\"\u00a0 —\u00a0\u00a0<\/b><\/span><\/span><\/span>T=5.408N<\/b><\/span><\/span><\/span><\/p>\n

16-<\/b><\/span><\/span><\/span> <\/b>Mesma corda (mesmo meio), a V \u00e9 a mesma.\u00a0\u00a0 —-\u00a0\u00a0 considerando a freq\u00fc\u00eancia fundamental (\u03bb=2L)\u00a0 —\u00a0\u00a0\u03bb<\/b><\/span><\/span><\/span>Mi<\/b><\/span><\/span><\/sub><\/span>f<\/b><\/span><\/span><\/span>Mi<\/b><\/span><\/span><\/sub><\/span>=\u03bb<\/b><\/span><\/span><\/span>L\u00e1<\/b><\/span><\/span><\/sub><\/span>f<\/b><\/span><\/span><\/span>L\u00e1<\/b><\/span><\/span><\/sub><\/span>\u00a0 —\u00a0 2L<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>.660=2L<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span>.880\u00a0 —\u00a0\u00a0<\/b><\/span><\/span><\/span>L<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span>\/L<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>=3\/4<\/b><\/span><\/span><\/span><\/p>\n

17-<\/b><\/span><\/span><\/span> <\/b>a) T=2,5.10<\/b><\/span><\/span><\/span>-3<\/b><\/span><\/span><\/sup><\/span>s\u00a0 —\u00a0 f=1\/T\u00a0 —\u00a0 f=1\/2,5.10<\/b><\/span><\/span><\/span>-3<\/b><\/span><\/span><\/sup><\/span>\u00a0 —\u00a0 f=400Hz<\/b><\/span><\/span><\/span><\/p>\n

b) Nota desafinada \u2013 T<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>\u00a0\u2013 f=400Hz –\u00a0\u00b5=5,0.10<\/b><\/span><\/span><\/span>-3<\/b><\/span><\/span><\/sup><\/span>kg\/m \u2013 som fundamental n=1\u00a0 —\u00a0 f<\/b><\/span><\/span><\/span>n<\/b><\/span><\/span><\/sub><\/span>=n\/2L\"\"\u00a0 —\u00a0 400=1\/2.1\"\" — T<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>=3.200N<\/b><\/span><\/span><\/span><\/p>\n

Nota afinada \u2013 T<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span>\u00a0\u2013 f=440Hz –\u00a0m=5,0.10<\/b><\/span><\/span><\/span>-3<\/b><\/span><\/span><\/sup><\/span>kg\/m \u2013 som fundamental n=1\u00a0 —\u00a0 f<\/b><\/span><\/span><\/span>n<\/b><\/span><\/span><\/sub><\/span>=n\/2L\"\"\u00a0 —\u00a0 440=1\/2.1\"\"\u00a0 —\u00a0 T<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span>=3.872N\u00a0<\/b><\/span><\/span><\/span><\/p>\n

O aumento de tens\u00e3o na corda ser\u00e1\u00a0\u0394T=T<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span>\u00a0\u2013 T<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>=3.872 \u2013 3.200=<\/b><\/span><\/span><\/span>672N<\/b><\/span><\/span><\/span><\/p>\n

18-<\/b><\/span><\/span><\/span> <\/b>a) som fundamental\u00a0 —\u00a0\u00a0\u03bb<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>\/2=50\u00a0 —\u00a0\u00a0\u03bb<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>=1m\u00a0 —\u00a0 V=\u03bb<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>f<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>=1.500\u00a0 —<\/b><\/span><\/span><\/span>\u00a0 V=500m\/s<\/b><\/span><\/span><\/span><\/p>\n

b) V=\u03bbf\u00a0 —\u00a0 500=0,5f\u00a0 —\u00a0\u00a0<\/b><\/span><\/span><\/span>f=1000Hz<\/b><\/span><\/span><\/span><\/p>\n

19-<\/b><\/span><\/span><\/span> <\/b>V e L s\u00e3o constantes (mesma corda).<\/b><\/span><\/span><\/span><\/p>\n

f<\/b><\/span><\/span><\/span>n+1<\/b><\/span><\/span><\/sub><\/span>=(n + 1)V\/2L\u00a0 —\u00a0 f<\/b><\/span><\/span><\/span>n<\/b><\/span><\/span><\/sub><\/span>=nV\/2L\u00a0 —\u00a0 f<\/b><\/span><\/span><\/span>n+1<\/b><\/span><\/span><\/sub><\/span>\/f<\/b><\/span><\/span><\/span>n<\/b><\/span><\/span><\/sub><\/span>\u00a0= (n+1)V\/2LX2L\/nV\u00a0 —\u00a0\u00a0<\/b><\/span><\/span><\/span>f<\/b><\/span><\/span><\/span>n+1<\/b><\/span><\/span><\/sub><\/span>\/f<\/b><\/span><\/span><\/span>n+\u00a0<\/b><\/span><\/span><\/sub><\/span>= (n+1)\/n<\/b><\/span><\/span><\/span><\/p>\n

20-<\/b><\/span><\/span><\/span> <\/b>f<\/b><\/span><\/span><\/span>n<\/b><\/span><\/span><\/sub><\/span>=nf<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>\u00a0 —\u00a0 f<\/b><\/span><\/span><\/span>n<\/b><\/span><\/span><\/sub><\/span>=n.100 (n=2,3,4,5)\u00a0\u00a0 R- C<\/b><\/span><\/span><\/span><\/p>\n

21-<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>Rela\u00e7\u00e3o entre as equa\u00e7\u00f5es da frequ\u00eancia e da velocidade\u00a0 —\u00a0 f<\/b><\/span><\/span><\/span>n<\/b><\/span><\/span><\/sub><\/span>=n.V\/2L\u00a0 —\u00a0 V=\u221a(T\/<\/b><\/span><\/span><\/span>\u03bc<\/b><\/span><\/span><\/span><\/span>)\u00a0 —\u00a0 f<\/b><\/span><\/span><\/span>n<\/b><\/span><\/span><\/sub><\/span>=1\/2L. \u221a(T\/<\/b><\/span><\/span><\/span>\u03bc<\/b><\/span><\/span><\/span><\/span>)\u00a0 — para a corda 1\u00a0 —\u00a0 f<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>=1\/2L. \u221a(T\/<\/b><\/span><\/span><\/span>\u03bc<\/b><\/span><\/span><\/span><\/span>)\u00a0 —\u00a0 36=1\/2.(0,60).\u221a(40\/<\/b><\/span><\/span><\/span>\u03bc<\/b><\/span><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>)\u00a0 —\u00a0 (72.0,60)<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>=(\u221a40\/<\/b><\/span><\/span><\/span>\u03bc<\/b><\/span><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>)<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>\u00a0 —\u00a0\u00a0<\/b><\/span><\/span><\/span>\u03bc<\/b><\/span><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>=0,021\u00a0 —\u00a0 frequ\u00eancia fundamental da corda 2\u00a0 —<\/b><\/span><\/span><\/span><\/p>\n

f\u2019<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>=1\/2L. \u221a(T<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span>\/<\/b><\/span><\/span><\/span>\u03bc<\/b><\/span><\/span><\/span><\/span>)\u00a0 —\u00a0 f\u2019<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>=1\/2.(0,40).\u221a(90\/0,021)\u00a0 —\u00a0<\/b><\/span><\/span><\/span>\u00a0f\u2019<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>=81 Hz<\/b><\/span><\/span><\/span><\/p>\n

22-<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>V=\u221aT\/<\/b><\/span><\/span><\/span>\u03bc<\/b><\/span><\/span><\/span><\/span>=\u221a(240\/2,4.10<\/b><\/span><\/span><\/span>-4<\/b><\/span><\/span><\/sup><\/span>)\u00a0 —\u00a0 V=\u221a(100.10<\/b><\/span><\/span><\/span>4<\/b><\/span><\/span><\/sup><\/span>)\u00a0 —\u00a0 V=10.10<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sup><\/span>\u00a0 —\u00a0 V=10<\/b><\/span><\/span><\/span>3<\/b><\/span><\/span><\/sup><\/span>=1.000m\/s\u00a0 —<\/b><\/span><\/span><\/span>\u00a0R- A<\/b><\/span><\/span><\/span><\/p>\n

23-<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>Velocidade de propaga\u00e7\u00e3o da onda \u00a0—\u00a0 V=<\/b><\/span><\/span><\/span>\u03bb<\/b><\/span><\/span><\/span><\/span>.f\u00a0 —\u00a0 V=50.0,5\u00a0 —\u00a0 V=25m\/s\u00a0 —\u00a0 V=\u2206S\/\u2206t\u00a0 — 25=10\/\u2206t\u00a0 —\u00a0 \u2206t=0,4s\u00a0\u00a0<\/b><\/span><\/span><\/span>R- B<\/b><\/span><\/span><\/span><\/p>\n

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

24-<\/b><\/span><\/span><\/span>\u00a0<\/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<\/b><\/span><\/span><\/span>\u00a0R- A<\/b><\/span><\/span><\/span><\/p>\n

25-<\/b><\/span><\/span><\/span> <\/b>Observe abaixo a express\u00e3o gen\u00e9rica para n harm\u00f4nicos:<\/b><\/span><\/span><\/span><\/p>\n

en\u00e9simo harm\u00f4nico\u00a0 —\u00a0 (\u201cn + 1\u201d n\u00f3s e\u00a0n fusos)<\/b><\/span><\/span><\/span><\/p>\n

n.\u03b3<\/b><\/span><\/span><\/span>n<\/b><\/span><\/span><\/sub><\/span>\/2=L\u00a0 —\u00a0\u00a0.\u03b3<\/b><\/span><\/span><\/span>n<\/b><\/span><\/span><\/sub><\/span>\u00a0=2L\/n\u00a0 —\u00a0 V=.\u03b3<\/b><\/span><\/span><\/span>n<\/b><\/span><\/span><\/sub><\/span>.f<\/b><\/span><\/span><\/span>n<\/b><\/span><\/span><\/sub><\/span>\u00a0 —\u00a0 f<\/b><\/span><\/span><\/span>n<\/b><\/span><\/span><\/sub><\/span>=V\/\u03b3<\/b><\/span><\/span><\/span>n<\/b><\/span><\/span><\/sub><\/span>\u00a0 —\u00a0<\/b><\/span><\/span><\/span>\u00a0f<\/b><\/span><\/span><\/span>n<\/b><\/span><\/span><\/sub><\/span>=nV\/2L<\/b><\/span><\/span><\/span>\"\"<\/p>\n

Lembrando que\u00a0<\/b><\/span><\/span><\/span>f<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>=V\/2L<\/b><\/span><\/span><\/span>\u00a0 —\u00a0<\/b><\/span><\/span><\/span>\u00a0f<\/b><\/span><\/span><\/span>n<\/b><\/span><\/span><\/sub><\/span>=nf<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span><\/p>\n

Se voc\u00ea tiver dois harm\u00f4nicos consecutivos\u00a0 —\u00a0 f<\/b><\/span><\/span><\/span>n<\/b><\/span><\/span><\/sub><\/span>=n.V\/2L e f<\/b><\/span><\/span><\/span>(n + 1)<\/b><\/span><\/span><\/sub><\/span>=(n + 1).V\/2L\u00a0 —\u00a0 \u2206f=(n + 1).V\/2L \u2013 n.V\/2L\u00a0 —\u00a0 \u2206f=nV\/2L +<\/b><\/span><\/span><\/span><\/p>\n

V\/2L \u2013 nV\/2L\u00a0 —\u00a0\u00a0 \u2206f=V\/2L\u00a0 —\u00a0 175 \u2013 150=V\/2.2\u00a0 —\u00a0 V=100m\/s\u00a0 —\u00a0<\/b><\/span><\/span><\/span>\u00a0R- A<\/b><\/span><\/span><\/span><\/p>\n

 <\/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 Cordas vibrantes – Harm\u00f4nicos 01- 75 oscila\u00e7\u00f5es \u2013 30s\u00a0 —\u00a0 1 oscila\u00e7\u00e3o\u00a0 —\u00a0 T=30\/75s\u00a0 —\u00a0 f=1\/T\u00a0 —\u00a0 f=75\/30\u00a0 —\u00a0 f=2,5Hz — fn=nf1\u00a0 — supondo n=1\u00a0 —\u00a0 f1=2,5Hz\u00a0 —\u00a0 a pr\u00f3xima ocorre quando n=2\u00a0 —\u00a0 f2=2f1\u00a0 —\u00a0 f2=2.2,5\u00a0 —\u00a0\u00a0f2=5Hz\u00a0\u00a0\u00a0 R- D 02- L=0,6m\u00a0 —\u00a0 som fundamental (1 fuso)\u00a0 — n=1\u00a0 —\u00a0 fn=nV\/2L\u00a0 —\u00a0 f1=V\/2L\u00a0<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":2386,"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-2390","page","type-page","status-publish","hentry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/2390","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=2390"}],"version-history":[{"count":4,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/2390\/revisions"}],"predecessor-version":[{"id":10900,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/2390\/revisions\/10900"}],"up":[{"embeddable":true,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/2386"}],"wp:attachment":[{"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/media?parent=2390"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}