soundspeed

Sound speed, or the speed of sound, is the rate at which small pressure disturbances propagate through a medium. It depends on the medium’s stiffness (elastic properties) and density, and on conditions such as temperature and phase. In fluids (gases and liquids) the traveling waves are primarily compressional, while in solids both longitudinal and transverse waves can propagate.

In gases, the speed of sound can be approximated by c = sqrt(γRT/M) or equivalently c = sqrt(γp/ρ), where γ is the heat capacity ratio, R is the gas constant, T is temperature, M is molar mass, p is pressure, and ρ is density. At sea level, dry air travels about 343 meters per second at 20°C, and roughly 331 meters per second at 0°C. The speed increases with temperature and humidity, though humidity has a smaller effect than temperature.

In liquids, speeds are higher due to greater stiffness relative to density. For water, the speed is about 1480–1500 meters per second, depending on temperature. In seawater it is nearby 1500 meters per second. In solids the speeds are substantially higher and depend on the material’s elastic moduli and density; for example, longitudinal waves in steel travel around 5000–6000 meters per second, while transverse waves travel more slowly.

Key relationships and limitations: the speed of sound rises with stiffness and falls with density. In a vacuum there is no medium to transmit sound, so sound cannot propagate. The concept is widely used in acoustics, meteorology, sonar and ultrasound, nondestructive testing, and aviation, where the Mach number compares an object’s speed to the local sound speed.