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História Da Acústica 1 Universidade de São Paulo Instituto de Física de São Carlos - IFSC FFI0210 Acústica Física História da Acústica 1 Prof. Dr. José Pedro Donoso Agradescimentos O docente da disciplina, Jose Pedro Donoso, gostaria de expressar o seu agradecimento as editoras LTC (livros Tecnicos e Científicos) e Cengage Learning pelo acesso às figuras dos livros textos: ”Fisica ” de Tipler & Mosca e “Fundamentos de Física ” de Halliday, Resnick e Walker (LTC) e “Principios de Física ” de Serway & Jewett (Cengage Learning). Datas e personagens na história da Acústica China: 270 A.C. padrão de altura ( pitch ) para música. Grecia e Roma Pitagoras Chrysippus Marco Vitruvius Severino Boethius (480 – 524) Século XVII Marin Mersenne (1588 – 1648) Pierre Gassendi (1582 – 1655) Robert Boyle (1626 – 1691) Robert Hooke (1635 – 1703) Joseph Sauveur (1653 – 1713) Franciscus Mario Grimaldi (1613 – 1663) Século XVIII Ernst Chladni (1756 – 1827) Isaac Newton (1642 – 1726) Giovanni lodovico Bianoni (1717 – 1781) Charles Marie de la Condamine (1701 – 1773) Richard Helsham (1680 – 1758) John W. Strutt (Lord Rayleigh) (1845 – 1919) Arthur Gordon Webster (1863 – 1923) Thomas Young (1773 – 1829) e Auguste Jean Fresnel (1788 – 1817) Métodos de analisis Isaac Newton (1642 – 1726) e Gottfried W. Leibniz (1646 – 1716) Joseph Louis Lagrange (1736 – 1813) James Bernoulli (1654 – 1705) e Johann Bernoulli (1667 – 1748) G.F.A. L’ Hôpital (1661 – 1704) e Gabriel Cramer (1704 – 1752) Leonhard Euler (1707 – 1783) e Jean Le Rond d’Alembert (1717 – 1783) Daniel Bernoulli (1700 – 1783) e Joseph Louis Lagrange (1736 – 1813) Pierre Simon Laplace (1749 – 1827) e Adrian Marie Legendre (1736 – 1833) Jean B. Joseph Fourier (1768 – 1830) e Simeon D. Poisson (1781 – 1840) Século XIX Simon Ohm (1789 – 1854) Hermann F.L. von Helmoltz (1821 – 1894) Wallace Clement Sabine (1868 – 1919) Século XX Paul Earl Sabine (1879 – 1958) Hale Johnson Sabine (1909 – 1981) Constantin Chilowsky (1880 – 1958) Paul Langevin (1872 – 1946) Vern O. Knudsen (1893 – 1974) Cyril M. Harris (1917 - ) Harvey Fletcher (1884 – 1990) Richard Henry Bolt (1911 – 2002) Leo Beranek (1914 - ) Carleen Hutchins (1911 - ) D.R. Raichel, The Science and applications of acoustics (2nd ed. Springer, 2006) Egito: musicistas tocando harpa, laude e um instrumento de sopro. Pintura da tumba de Nakht, necrópole de Tebas, 1350 a.C. Egito, Coleção Grandes Civilizações do Passado (Ediciones Folio, 2006) China Os sons foram classificados por timbre e por altura, e se especificaram várias escalas musicais. Isso, por sua vez, exigia uma afinação perfeita. Um sino devidamente afinado podia servir de padrão e faria com que outro sino tocasse em ressonância quando estivesse corretamente afinado. Em 270 a.C. Lin lun, ministro do imperador Huangundi, é encarregado de estabelecer um padrão de altura ( pitch ) para música. C.A. Ronan, Historia Ilustrada das Ciências , Universidade de Cambridge (Ed. Zahar, 1987) D.R. Raichel, The Science and applications of acoustics (2nd ed. Springer, 2006) M. Jing, J. Acoust. Soc. America 114, 1622 (2003) Robert Grosseteste foi a figura central na Inglaterra do importante movimento inteletual da primeira metade do século XIII. Consagrado bispo de Lincoln em 1253, tinha grande curiosidade das coisas naturais e escreveu importantes textos a respeito de optica, som e astronomia. Grande amante da música, trabalhou nas relações matemáticas entre as notas. No periodo da Renascença se destacou o engenheiro flamengo Simon Stevin . Trabalhou como engenheiro militar e fez contribuições à matemática (algebra) e à mecánica (estática e hidroestática). Seus textos sobre escalas musicais continham a primeira descrição no Ocidente da afinação de “igual temperamento”. C.A. Ronan, Historia Ilustrada das Ciências Universidade de Cambridge (Ed. Zahar, 1987) Grecia As pesquisas dos Pitágoras e seus discípulos se referem a natureza do som e a teoria matemática da escala. Com base nos acordes produzidos por cordas vibrantes de diferentes comprimentos, a Escola pitagórica construiu a escala a partir dos números inteiros pequenos, suas frações e potências. A escala pitagórica foi reformada por Aristóxeno (360 – 300 a.C.) por razões baseadas na música e na exigência do ouvido. René Taton (diretor), História Genral de las Ciências (Ed. Destino, Barcelona,1971) Ian Johnston, Measured Tones (Taylor & Francis, 2002) Grecia Para Euclides (s. III), a altura do som aumenta com o número de movimentos (choques) produzidos. Dois sons podem ser consoantes ou dissoantes. Na ultima parte do tratado, sobre os instrumentos de corda, se admite tacitamente que o número das vibrações é inversamente proporcional ao comprimento da corda em vibração. Euclides História Genral de las Ciências René Taton (diretor) Ediciones Destino, Barcelona (1971) Teatro grego de Epidauros R.S. Shankland, Physics Today (October 1973) L.J. Arizmendi, Tratado Fundamental de Acustica en la Edificación (Ed. Univ. Navarra, Pamplona,1980) Arquimedes de Siracusa determinou a área da superfície esférica e estabeleceu a chamada Lei do inverso do quadrado da distância para a intensidade acústica e luminosa. Herón (100 a.C.), indicou que o ângulo de incidência ao chocar o som contra um sólido seria igual ao ângulo de reflexão. Desta forma, foram traçados os dois princípios fundamentais da Acústica Geométrica , cuja culminação arquitetônica é o teatro grego. Eles foram os primeiros a perceber que audição e visibilidade são dois conceitos inseparáveis Guido D'Arezzo (995-1050) monge beneditino regente do coro da Catedral de Arezzo (Toscana, Italia). Ele atribuiu as notas musicais pelas letras ut , re , mi , fa , sol , la , letras que coincidem com os versos de hino composto em homenagem a São João Batista: Ut queant laxis Re sonare fibris Mi ra gestorum Fa muli tuorum Sol ve polluti La bii reatum J. Perez Miñana. Compendio práctico de acústica Sancte Ioannes (Ed. Labor, 1969) A nota si aparece no século XVI (chamada inicialmente bi ). Em 1673, numa peça de Bononcini, aparece a letra do , que substitui a ut . Idade média As condições acústicas das primeiras catedrais era totalmente inadequadas. As abóbadas e cupulas provocam uma série de reflexões e concentrações de som que dificultam a audição. O estilo gótico aumentou o problema pois, ao crescer as proporções aumentaram as distância que percorre o som e as reflexões sucessivas, aparecendo os ecos . Isto favorecia o canto gregoriano ao reforçar a sensação de grandiosidade. Com o Renacimento , se interrompe a sede por volumes desmedidos do estilo gótico. Os templos tem proporções harmoniosas com abundante ornamentação. Catedral de Bourges (França,1195 a 1255) J. Perez Miñana. Mervilleuses Cathédrales de France Compendio práctico de acústica Editions Princesse, Paris, 1986 (Ed. Labor, 1969) Fora dos templos, o canto era cultivado apenas por trovadores. No ano de 1207 celebrou-se no castelo de Wartburgo (Sajonia), um concurso de canto entre trovadores. Este pode ser considerado o primeiro local utilizado para interpretações paganas do canto. Em 1576 se construi em Londres o primeiro teatro inglés, que em 1599 foi substituido pelo Globe Theater . A partir de 1600, a música apresenta uma grande riqueza de efeitos e filigramas. Aparecem a melodia, a candenza e o compasso, ampliando as possibilidades musicais. J. Perez Miñana. Compendio práctico de acústica Galileo Galilei (1564 – 1642) Galileo realizando demostrações. Pintura de Guiseppe Bezzouli (Zoological Museum, Florencia) Verificou que a sensação de altura musical relacionava-se diretamente à freqüência. Esta percepção marca o início da física da música em sua concepção atual. O.J. Abdounur, Matemática e Música (Escrituras editora, SP, 1999) Robert Boyle Em 1660, extraiu o ar de um vaso de vidro onde havia um relógio despertador. Ele descubriu que o som precisa de um meio para se propagar. As ondas de som são transmitidas através do ar e de outros materiais (gasosos, líquidos e sólidos). Uma campainha, por exemplo, ao ser tocada fará vibrar as moléculas de ar mais próximas. Se a campainha é tocada dentro de uma campânula de vidro sem ar, não será escutado som nenhum. Som e Audição , Biblioteca Científica Life . José Olympio Editora, 1981 Marin Mersenne (1588-1648) Motivado pelo seu interesse em música, dedicou-se a pesquisa em acústica e as medidas da velocidade de propagação do som no ar. Em 1627 publicou L'harmonie universelle cuja abordagem teórico- prática contém relatos de experimentos engenhosos, estudos sobre o som e reflexões concernentes à relação entre matemática e música, pelo qual é considerado o pai da acústica . Ele foi o primeiro a determinar a freqüência de uma nota musical e descobriu que a relação da freqüência entre uma nota e sua oitava era respectivamente de 1 para 2. Ele explicou as características de colunas vibrantes de ar, bem como os fenômenos do eco e da ressonância. Estabaleceu a relação da frequência de uma corda tensionada: A.D. Pierce, Acoustics (AIP & Acoustic Soc America, 1981) 1 T O.J. Abdounur, Matemática e Música f = (Escrituras editora, SP, 1999) 2L µ Medidas da velocidade de propagação do som no ar 1636, Mersenne , utilizando instrumentos musicais e canhões: 316 m/s 1658, Gassendi , estabelece que vs independe do timbre e da intensidade do som 1666, Borelli a Viviane (discípulo de Galileo): 361 m/s 1687, Newton determina teoricamente 295 m/s a partir da Lei de Boyle 1708, o reverendo William Derham , desde a torre da igreja em Upminster (Essex), observa o disparo de um canhão em Blackheath, a 19 km de distância: 348 m/s 1738, Cassini, Römer, Picard e Huygens , disparos de canhão em 28 km: 347 m/s 1822 Prony, Arago, Bouyard, Mathieu, Gay-Lussac e Humboldt : 340.9 m/s 1905, Hebb (USA) utilizando a tecnica de Michelson: 331.41 m/s para o ar seco. M.E. Delany, Acustica 38 (1977) 201 Medidas da velocidade do som na água Jean-Daniel Colladon (1802-1893) e Charles Sturn (1803-1855) Lago de Genebra (1826, 1827). R.T. Beyer. Sounds of Our Times (Springer & AIP, 1999) A. Fischetti. Initiation à l´ Acoustique (Editions Belin, Paris, 2003) Velocidade do som na água A fonte do som era um sino que era golpeado debaixo da água ao mesmo tempo que explodiam uma pequena quantidade de pólvora.
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