Sound waves are mechanical vibrations that travel through a medium such as air, water, or solids. The understanding of sound is not the result of a single, sudden discovery; instead, it evolved over two millennia, starting as a philosophical concept before transitioning into a quantifiable physical phenomenon. This process moved from simple recognition of vibration to experimental measurement of its speed and, finally, to a rigorous mathematical definition of its wave nature.
Early Philosophical Understanding of Vibration
The earliest attempts to understand sound focused on its relationship to vibration and mathematics. This conceptual phase began in ancient Greece.
Pythagoras, in the 6th century BCE, made a foundational observation by connecting musical harmony to mathematical ratios. He discovered that consonant musical intervals corresponded to simple whole-number ratios when comparing the lengths of vibrating strings. For example, a string half the length of another produces a note one octave higher. This established that the pitch of a sound was determined by a measurable, numerical structure related to the source’s vibration.
Later, Aristotle, in the 4th century BCE, advanced the understanding of sound propagation beyond just the source. He proposed that sound was a movement of air, generated by the impact of one object against another. This idea suggested that the initial vibration thrust forward the adjacent air, propagating the disturbance. Aristotle’s concept implied that sound required a physical medium, like air, to travel, foreshadowing the modern definition of a mechanical wave.
The First Experimental Measurements of Sound Speed
The philosophical ideas about sound were transformed into quantifiable physics in the 17th century through systematic experimentation. The French mathematician and cleric Marin Mersenne was central to this shift, focusing on both the frequency of vibration and the speed of sound’s travel.
Mersenne became the first person to measure the absolute frequency of a musical note. He used the physical properties of the vibrating string to calculate the number of oscillations per second. His subsequent work, known as Mersenne’s Law, established the precise relationship between a string’s length, tension, and mass per unit length to its vibrational frequency. This confirmed that pitch is a function solely of frequency.
Mersenne also conducted some of the earliest experiments to determine the propagation speed of sound in air. His method involved timing the delay between seeing a visual event and hearing its corresponding sound over a known distance. Observers timed the interval between the flash of a distant cannon or musket firing and the moment the sound reached them.
His initial calculation in 1635 yielded a speed of about 448 meters per second. Subsequent attempts using echoes from walls produced a closer value of 316 meters per second. These experiments provided the first numerical estimates for the speed of sound, establishing it as a measurable physical constant.
Formalizing Sound as a Longitudinal Wave
The final step in understanding sound involved defining its mechanism of travel using a theoretical and mathematical framework. This formalization was largely accomplished by Isaac Newton in his 1687 work, Philosophiæ Naturalis Principia Mathematica.
Newton described sound as a wave propagating through a fluid medium, consisting of a series of alternating compressions and rarefactions. This definition established sound as a longitudinal pressure wave, meaning the particles in the medium vibrate parallel to the direction the wave is traveling. He developed a mathematical formula for the speed of sound based on the density and the elastic properties of the medium.
However, Newton made a flawed assumption in his calculation, treating the compressions and rarefactions as an isothermal process, meaning the temperature remained constant. This led his formula to predict a speed of sound in air of approximately 280 meters per second, which was less than the experimentally measured values.
The discrepancy was resolved over a century later by French mathematician Pierre-Simon Laplace. Laplace recognized that the rapid pressure changes happen too quickly for heat to be exchanged with the surroundings. He correctly argued that the process must be adiabatic. By incorporating the ratio of specific heats of air into Newton’s formula, Laplace’s correction brought the calculated theoretical speed into agreement with the measured experimental values. This correction solidified the modern understanding of sound as a fully defined physical wave governed by the principles of thermodynamics and classical mechanics.