Speed of sound

Sound travels at different speeds depending on what it's moving through and the conditions. In simple terms, it's how fast vibrations move. At 20 °C (68 °F), a sound wave in air moves at about 343 meters per second—that's roughly 1,125 feet per second, 1,235 kilometers per hour, 767 miles per hour, or 667 knots. Covering one kilometer takes about 2.92 seconds, and a mile takes about 4.69 seconds. Temperature matters a lot: at 0 °C (32 °F) in dry air at sea level pressure (14.7 psi), the speed drops to around 331 m/s (1,086 ft/s, 1,192 km/h, 740 mph, 643 kn). For an ideal gas, the speed depends only on temperature and composition. In dry air, frequency and pressure have a weak effect, causing slight deviations from ideal behavior.

In everyday talk, "speed of sound" usually means how fast sound waves travel through air. But the speed changes dramatically depending on the substance. Sound moves slowest in gases, faster in liquids, and fastest in solids. For instance, while air gives 343 m/s, fresh water at 20 °C carries sound at 1,481 m/s—over 4.3 times faster. In iron, it reaches 5,120 m/s, nearly 15 times faster than in air. Diamond, an exceptionally stiff material, pushes that to 12,000 m/s (39,000 ft/s), about 35 times the speed in air and close to the fastest possible under normal conditions.

Technically, the speed of sound is the speed of vibrations. In solids, sound waves come in two types: compression waves (like those in gases and liquids) and shear waves, which only exist in solids. Shear waves usually travel at a different speed than compression waves, as seen in seismology. For compression waves in solids, the speed depends on the medium's compressibility, shear modulus, and density. For shear waves, it depends only on the shear modulus and density.

In fluid dynamics, the speed of sound in a gas or liquid serves as a benchmark for how fast an object moves through that fluid. The ratio of an object's speed to the speed of sound in the same medium is called its Mach number. Objects moving faster than the speed of sound (Mach 1) are described as traveling at supersonic speeds.

**History**

The ancient Greek philosopher Archytas, a Pythagorean, believed that higher-pitched sounds travel faster. This view was accepted by some later thinkers, including those from the Academy and the Peripatetic school, and possibly Aristotle.

Isaac Newton's 1687 *Principia* calculated the speed of sound in air as 979 feet per second (298 m/s)—about 15% too low. The main reason was that he didn't account for the rapid temperature changes in a sound wave (now understood as an adiabatic process, not isothermal). To make his number match experiments, Newton invented corrections like the "crassitude of the solid particles of the air." Later, Lagrange and Euler tried and failed to fix the discrepancy. Pierre-Simon Laplace finally got it right. In his *Traité de mécanique céleste*, he used results from the 1819 Clément-Desormes experiment, which measured air's heat capacity ratio as 1.35. This brought theory and experiment close together. The modern value of 1.40 was found later, giving complete agreement.

During the 1600s, several attempts were made to measure the speed of sound accurately. In 1630, Marin Mersenne got two different results. Timing the interval between seeing a gun's flash and hearing its sound over a known distance (using a seconds pendulum), he found 1,380 Parisian feet per second (448 m/s). But when he measured the time between firing a gun and hearing its echo from a known reflecting surface, he got 970 Parisian feet per second. This led some to think echoed sound is slower than direct sound. Most later experimenters used only his first method.

In 1635, Pierre Gassendi measured 1,473 Parisian feet per second, and Robert Boyle got 1,125 Parisian feet per second. In 1650, G. A. Borelli and V. Viviani of the Accademia del Cimento found 350 m/s. In 1709, Reverend William Derham, rector of Upminster, published a more accurate figure: 1,072 Parisian feet per second. (The Parisian foot was 325 mm, longer than the modern international foot of 304.8 mm defined in 1959. At 20 °C, the speed of sound would be about 1,055 Parisian feet per second.) Derham used a telescope from the tower of St. Laurence Church in Upminster to watch the flash of a distant shotgun, then measured the time until he heard the shot with a half-second pendulum. He took measurements from several local landmarks, including North Ockendon church. He calculated distances by triangulation. He repeated the experiment many times under different conditions to see how wind, barometric pressure, temperature, and humidity affected the speed. He found that wind blowing toward the observer made sound faster, and wind blowing away made it slower. He mistakenly thought temperature had no effect because speeds were the same in summer and winter. He also wrongly concluded that rain and fog slowed sound down—a belief accepted until Tyndall disproved it.

Early measurements disagreed with each other, and researchers suspected wind and temperature were responsible. In 1740, G. L. Bianconi showed that the speed of sound in air increases with temperature. The Academy of...