Speed of Sound: Definition, Physics, Typical Values and Applications

Physical basis and formula

Sound in fluids is a longitudinal wave: particles oscillate back and forth parallel to the wave's travel direction. For an ideal gas the small-signal speed of sound a is determined by the medium's stiffness and inertia. Two common expressions are shown below; both are equivalent for an ideal gas. The thermodynamic form emphasizes temperature:

a = sqrt(γ R T)

In this expression, γ (gamma) is the ratio of specific heats at constant pressure and volume (about 1.4 for dry air), R is the specific gas constant for the gas (about 287 J·kg⁻¹·K⁻¹ for dry air), and T is the absolute temperature in kelvins. The same speed can also be written as a = sqrt(γ p / ρ), linking pressure p and density ρ.

Factors that affect the speed

• Temperature: warmer air transmits sound faster; colder layers slow it down—this is important in atmospheric acoustics and explains changes with altitude; see temperature effects and conditions in the stratosphere.
• Medium composition: different gases, liquids and solids have different elastic moduli and densities, so the same acoustic disturbance moves at different speeds.
• Humidity and pressure: added water vapour slightly raises the speed in air; at constant temperature, pressure has little effect for an ideal gas because density changes offset pressure changes.
• Wave type: in solids both longitudinal and transverse (shear) waves can travel, and shear waves generally move at different speeds than compressional waves.

Typical values and examples

Common reference speeds are useful for comparison. In air at 20 °C the speed is about 343 m/s. In fresh water it is roughly 1,500 m/s, and in many metals the compressional wave speed is several kilometres per second (for example on the order of 5–6 km/s in steel). Engineering and transport contexts use these values when designing sonar, ultrasound systems or evaluating aircraft performance. The term Mach number expresses an object's speed relative to the local speed of sound: Mach 1 equals the local sound speed; speeds above that are supersonic and speeds around five times greater are described as hypersonic.

History and development

Early theoretical estimates of sound speed date to the 17th–18th centuries. Sir Isaac Newton first derived a formula assuming isothermal compressions and obtained a value lower than measured. Pierre-Simon Laplace later corrected the theory by accounting for the adiabatic nature of rapid compressions and expansions, bringing prediction and experiment into agreement. Subsequent work refined measurements and extended understanding to different media and frequency ranges.

Applications and notable distinctions

Knowing the speed of sound is essential in many disciplines: sonar and underwater acoustics rely on accurate water speeds; medical ultrasound uses known propagation characteristics for imaging; nondestructive testing exploits wave speeds in solids to detect flaws; meteorology and atmospheric acoustics use variations of sound speed to study wind and temperature profiles. Seismology distinguishes P-waves (compressional) from S-waves (shear), which travel at different speeds through Earth’s interior. Finally, practical engineering considers that the local speed of sound changes with temperature and composition, so Mach-number-based performance must use local rather than fixed reference values.

For further reading on the physical derivation, typical numerical tables, and practical measurement techniques consult introductory acoustics texts and specialized references. Links above indicate general topics and contexts where the speed of sound matters.