One of the first discoveries regarding sound was made in the sixth century B.C. by the Greek mathematician and philosopher Pythagoras. He noted the relationship between the length of a vibrating string and the tone it produces—what is now known as the first law of strings. Pythagoras may also have understood that the sensation of sound is caused by vibrations. Not long after his time it was recognized that this sensation depends on vibrations traveling through the air and striking the eardrum.
About 1640 the French mathematician Marin Mersenne conducted the first experiments to determine the speed of sound in air. Mersenne is also credited with discovering the second and third laws of strings. In 1660 the British scientist Robert Boyle demonstrated that the transmission of sound required a medium—by showing that the ringing of a bell in a jar from which the air had been pumped could not be heard.
Ernst Chladni, a German physicist, made extensive analyses of sound-producing vibrations during the late 1700's and early 1800's. In 1801 the French mathematician Fourier discovered that such complex waves as those produced by a vibrating string with all its overtones consist of a series of simple periodic waves.
Much work on waves in general was done during the 19th century. Thomas Young, an English physicist, did research especially on diffraction and interference. Christian Johann Doppler of Austria formulated the mathematical relationship between the actual and perceived frequencies of waves when the source of the waves is moving relative to the observer.
An important contribution to the understanding of acoustics was made by Wallace Clement Sabine, a physicist at Harvard University, in the late 1890's. Sabine was asked to improve the acoustics of the main lecture hall in Harvard's Fogg Art Museum. He was first to measure reverberation time—which he found to be 5 1/2 seconds in the lecture hall. Experimenting first with seat cushions from a nearby theater, and later with other sound-absorbing materials and other methods, Sabine laid the foundation for architectural acoustics. He designed Boston Symphony Hall (opened 1900), the first building with scientifically formulated acoustics.
In the second half of the 20th century, the rising level of noise in the modern world—particularly in urban areas—prompted a whole new series of investigations, dealing in large part with the physiological and psychological effects of noise on humans.