Speed of Sound Calculator

The speed of sound in air depends primarily on temperature. Warmer air has more energetic molecules that transmit pressure waves faster. The standard formula is c = 331.3 × sqrt(1 + T/273.15) m/s, where T is in °C. Humidity has a very small effect (moist air is very slightly faster than dry air at the same temperature) and is often ignored in basic calculations. Pressure alone does not significantly change the speed of sound in an ideal gas because, while higher pressure increases the restoring force on displaced molecules, it also increases density proportionally.

Sound travels as a compression wave through the elastic properties of a medium. In solids, atoms are tightly bound to each other with strong intermolecular forces, so pressure disturbances propagate very quickly. In liquids, molecules are close but less rigidly bonded, so sound travels slower than in solids but faster than in gases. In gases, molecules are widely spaced and interact only during brief collisions, making propagation slowest. Steel conducts sound at about 5,960 m/s, water at about 1,480 m/s, and air at sea level at around 343 m/s at 20°C.

At higher altitudes, air temperature generally decreases (in the troposphere), so the speed of sound also decreases. At sea level and 15°C (standard atmosphere), the speed of sound is approximately 340 m/s. At 11 km altitude (tropopause), the temperature is about -56.5°C and the speed of sound is approximately 295 m/s. This is why aircraft are described in terms of Mach number (speed relative to local sound speed) rather than absolute airspeed, because the same Mach number represents a different airspeed at different altitudes.

The speed of light in a vacuum is approximately 299,792,458 m/s, roughly 874,000 times faster than the speed of sound in air at 20°C (343 m/s). This enormous difference is why you see a lightning flash before you hear the thunder: the light arrives almost instantly, while sound takes about 3 seconds per kilometre. In water the ratio is smaller (light is about 200,000 times faster than sound in water), and in dense solids like steel, sound is still about 50,000 times slower than light.

A sonic boom is caused when an object travels at or above the speed of sound (Mach 1). As the object moves, it creates pressure waves that propagate outward spherically. When the object reaches or exceeds the speed of sound, it outruns these waves, which pile up into a conical shockwave called a Mach cone. Observers on the ground hear a sharp double boom as the shockwave passes. At Mach 1 (the sound barrier), the cone is perpendicular to the direction of travel; at higher Mach numbers the cone becomes more acute. Sonic booms are continuous during supersonic flight, not just at the moment of breaking the sound barrier.