Aristotle (384-322 B.C.), in his treatise On the Soul, explains how sound is transmitted by colliding of bodies with one another and the air produces sound, and recognized that a medium, such as water or air, was necessary condition of hearing. He understood sound as a periodic disturbance of the air and related the length of the wave to the length of the sounding pipe.
Later in the fifth century A.D., Boethius (480-525), following the Greek Aristotlian tradition, stated even more explicitly a nascent "wave theory" of sound.
"14. Let us now speak of the method of hearing. In the case of sounds something of the same sort takes place as when a stone is thrown out and falls onto a pool or calm water. The stone first produces a wave with a very small circumference. Then it causes the waves to spread out in ever wider circles unitil the motion, growing weaker as the waves spread out, finally ceases. The later and larger waves, the weaker the impluse with which it breaks. Now if there is an object that can block the waves as they grow larger, the motion is at one reversed, and forced back, in the same series of waves, to the center from which it originated. In same way, then, when air is struck and produces a sound, it impels other air next to it and in a certain way sets a rounded wave of air in motion, and is thus dispersed and strikes simultaneously the hearing of all who are standing around. And the sound is less clear to one who stands further away since the wave of impelled air which comes to him is weaker."In his book on Music he connects the frequency of the vibrations with pitch:
"...the same string, if it is tightened further, gives a higher pitched sound; if it is loosened, a sound of a lower pitch. For when it is tigher it renders a swifter pulse and returns more quickly. striking the air more frequently and more densely."
Robert Grosseteste (c.1168-1253) attempted to formulate a geometrical and almost mechanical conception of the rectilinear propagation of sound by a series of waves and pulses. In his commentary on Aristotle's Posterior Analytics, book 2, chapter 4, he describes how, when a sounding body is struck violently, it is set in vibration for a time because its violent motion and a "natural power" alternatively send the parts back and forth, each overshooting the natural position. These vibrations are transmitted through the surrounding air.
"Hence, when the sounding body is struck and vibrating, a similar vibration and similar motion must take place in the surrounding contiguous air, and this generation progresses in every direction in straight lines." If the propagation strikes an obstacle, it is forced to "regenerate itself by turning back. For the expanding parts of the air colliding with the obstacle must necessarily expand in the reverse direction,..., and this is an echo."
Galilei Galileo (1564-1642) described the dependence of pitch of a tone upon frequency. He understood that sound is due to the vibrations in the air falling on the eardrum, and in one of his dialogues he explains the concord and dissonance by the concurrence or conflict of such vibrations. He showed how the vibrations causing sound could be made visible and how the relative length of sound waves be measured.
There was no systematic scientific treatment of sound until the seventeenth century, when Pere Marin Mersenne (1588-1648), a follower of Galileo, friend of Descartes, and indefatigable correspondent on scientific matters, made the subject his own. Among his discoveries were the law of vibrating strings, that is, the frequency of the tone emitted by a string depends not only on the length, but on the tension and mass of the string. Mersenne also determined the speed of sound. He observed that the speed of sound is perceptibly slower than the speed of light; anyone watching a man with an axe cutting wood, finds that the sounds of the axe hitting the wood arrives much later after the sight of his impact which produce them, depending upon how far away it is. Mersenne used this fact to measure the speed of sound in air. In his day some philosophers held that sight is instantaneous, that is, the speed of light is infinite, others thought that the time (although very short) is required for it to travel from the object to the eye. Mersenne assumed that the time, if any, for the transmission of light is negligible compared with that required by sound. His method was to measure the time of the interval between the flash of the gun and the sound of gun and divide into the distance between them. He found that speed of sound in air was about 1000 ft/sec.
Robert Boyle (1627-1691) was the first to demonstrated that sound cannot travel in the absence of matter, by showing that a bell ringing inside an evacuated jar could not be heard.
Robert Hooke (1635-1703) demonstrated experimentally that each musical sound is characterized by a definite number of air vibrations per second and determined the speed of sound (about 1100 ft/sec.).
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