THE SCIENCE AND APPLICATIONS OF ACOUSTICS - H. H. Arnold ...

2 1. A Capsule History of AcousticsWith sound as a major factor affecting human lives, it was only natural for interestin the science of sound, or acoustics, to emerge. In the twenty-seventh centuryBCE, Lin-lun, a minister of the Yellow Emperor Huangundi, was commissionedto establish a standard pitch for music. He cut a bamboo stem between the nodesto make his fundamental note, resulting in the “Huang-zhong pipe”; the othernotes took their place in a series of twelve standard pitch pipes. He also tookon the task of casting twelve bells in order to harmonize the five notes, so asto enable the composing of regal music for royalty. Archeological studies of theunearthed musical instruments attested to the high level of instrument design andthe art of metallurgy in ancient China. Approximately 2000 bce, another Chinese,the philosopher Fohi, attempted to establish a relationship between the pitch of asound and the five elements: earth, water, air, fire, and wind. The ancient Hindussystematized music by subdividing the octave into 22 steps, with a large wholetone containing four steps, a small tone assigned three, and a half tone containingtwo such steps. The Arabs carried matters further by partitioning the octave into17 divisions. But the ancient Greeks developed musical concepts similar to thoseof the modern Western world. Three tonal genders—the diatonic, the chromatic,and the enharmonic—were attributed to the gods.Observation of water waves may have influenced the ancient Greeks to surmisethat sound is an oscillating perturbation emanating from a source over large distancesof propagation. It cannot have failed to attract notice that the vibrations ofplucked strings of a lute can be seen as well as felt. The honor of being the earliestacousticians probably falls to the Greek philosopher Chrysippus (ca. 240 bce),the Roman architect-engineer Vitruvius (also known as Marcus Vitruvius Pollio,ca. 25 bce), and the Roman philosopher Severinus Boethius (480–524). Aristotle(384–322 bce) stated in rather pedantic fashion that air motion is generated bya source “thrusting forward in like movement the adjoining air, so that soundtravels unaltered in quality as far as the disturbance of the air manages to reach.”Pythagoras (570–497 bce) observed that “air motion generated by a vibrating bodysounding a single musical note is also vibratory and of the same frequency as thebody;” and it was he who successfully applied mathematics to the musical consonancesdescribed as the octave, the fifth and the fourth, and established the inverseproportionality of the length of a vibrating string with its pitch. The forerunner ofthe modern megaphone was used by Alexander the Great (400 bce) to summonhis troops from distances as far as 15 km.The principal laws of sound propagation and reflection were understood bythe ancient Greeks, and the echo figured prominently in a number of classicaltales. Quintillianus demonstrated with small straw segments the resonance of astring in air. Vitruvius, after making use of the spread of circular waves on awater’s surface as an example, went on to explain that true sound waves travelin a three-dimensional world not as circles, but rather as outwardly spreadingspherical waves. He also described the placement of rows of large empty vasesfor the purpose of improving the acoustics of ancient theaters. While there may besome question if such vases have actually been employed in these theaters (sincearcheological excavations have failed to disclose their shards), it does presage