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Acoustics

DEFINITION OF ACOUSTICS

Acoustics is defined as the science of sound. The word comes from the Greek acoustikos, meaning “for hearing.”

Hearing is not limited to the human species. It is crucial in the animal world, as it enables them to detect an incoming danger or help pinpoint prey. More to the point, speech is used by many species, especially humans, for communication.

In the antique world acoustics was sometimes considered the science of sciences. Nowadays, it features numerous widely branches ranging, for example, physical acoustics, building acoustics, underwater acoustics, etc. A quite comprehensive list can be found in [1, 2]. Basically, when dealing with acoustics, three entities are involved: a source, a propagation medium, and a receiver. The source converts energy into vibrations of the propagation medium; it can be, for example, a vibrating rod or a surface. The propagation medium can be solid (e.g., metal, wood), liquid (e.g., water), or gas (e.g., air).

BRIEF HISTORY

The reader interested in the history of acoustics can find more developed information in references [3-6]. Here is only a brief reminder of a few points of interest.

In the antique world acoustics was sometimes considered the science of sciences. Musical acoustics were studied by scientists and philosophers who dreamed to discover the secrets of world order. During his investigations of musical intervals, Pythagoras (6th century BC) discovered harmonics. Vitruvius wrote a treatise featuring considerations on theatres, including echoes and reverberation (20 BC); he also compared sound propagation to the circles in water. Aristotle explained wave motion as contractions and expansions of air bumping into the one next to it.

The knowledge of the Greeks was passed on to the Romans and the Arabs, with the latter developing during the Middle Ages. Later the Renaissance saw the development of architectural acoustics and musical acoustics again.

Kircher (1602-1680) worked on sound propagation. While he wrongly concluded that no propagation medium was necessary, he also worked in architectural acoustics regarding the focusing by vaulted ceilings and the amplification effect by the bell of brass instruments.

Mersenne (1588-1648) managed to measure the sound propagation speed in 1640 using an artillery gun; he found that attenuation was a function of the distance to the power 2. He also found that the resonance frequency of a string was inversely proportional to its length and proportional to the square root of its tension [7]. Using both a handheld gun (generating high-pitched sounds) and an artillery gun (generating low-pitched sounds)

Gassendi (1592-1655) experimentally proved that speed propagation was independent of frequency. Huygens (1629-1695) showed that sound is an undulatory phenomenon, and Newton developed a mathematical formulation of the propagation of sound with an expression of the sound speed. Sauveur (1653-1716) looked at the composition of sounds and distinguished between the fundamental and its harmonics, whose decomposition defines tone color. He also defined nodes (locations where there is no elongation) and antinodes (locations where the elongation is maximal), and used the term acoustics to cover the science of sound. Bernoulli (1700-1782) explained the coexistence of small oscillations too.

With the development of mathematics in the 18th century, serious work was undertaken regarding sound propagation. D’Alembert (1717-1783), Euler (1707-1783), and Lagrange (1736-1813) developed the formal wave propagation equations. And Fourier (1768-1831) proposed his harmonic analysis of sound. Later developments included sound propagation in liquids (Sturm and Colladon in 1827) and solids (Hassenfratz in 1794 and Biot in 1808), as well as membrane or plate vibrations that were experimentally demonstrated by Chladni and theoretically investigated by Germain (1815), Poisson, and Clebsch.

The 19th century saw a significant interest in the perception of sound. Ohm showed that the hearing mechanism could distinguish frequencies (1843), and Corti proposed a model of the inner ear in 1851. Fechner published his Elements of Psychophysics (1860), where the relationship between sensation and excitation was investigated. Helmholtz (1821-1894), who was both a physicist and a physiologist, published his physiological theory of music (1877). Physical acoustics were not forgotten as Lord Rayleigh (1842-1919) published his Theory of Sound (1877) and Kundt (1839-1894) worked on resonances and stationary waves in tubes.

The 20th century saw an increase of interest in computational matters. As soon as 1901, the Boston Symphony Hall was the first such facility to be designed (by none other than Sabine) using acoustic computations. With the availability of computational methods and new technology, a first attempt at active noise cancellation was made in 1934 by Olsen, and Cremer developed the theory of sound transmission through a wall (1942).

 
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