Speed of Sound Calculator
Find the speed of sound in different media at a given temperature. Get results in meters per second, miles per hour, kilometers per hour, and Mach number.
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The Physics Behind Sound Speed
Sound is a mechanical wave that travels by vibrating the molecules of the medium it passes through. Unlike light, which can travel through a vacuum, sound requires a physical substance: gas, liquid, or solid. The speed at which it propagates depends on two properties of that substance: its density and its elastic stiffness.
In gases like air, the speed follows the formula v = 331.3 + 0.606T for temperature T in Celsius. This simplified equation works well for everyday temperatures between -40°C and 60°C. The full thermodynamic formula involves the ratio of specific heats, the gas constant, and absolute temperature, but the linear approximation is accurate enough for most practical purposes.
In solids and liquids, the speed depends on the bulk modulus (resistance to compression) divided by the density, then taking the square root. This is why stiff, dense materials like steel carry sound so rapidly.
Speed of Sound in Different Media
The variation in sound speed across materials is dramatic. Air at 20°C carries sound at 343 m/s. Water at the same temperature carries it at 1,482 m/s, about 4.3 times faster. Steel reaches 5,960 m/s, aluminum 6,420 m/s, and glass about 5,640 m/s. The pattern is clear: stiffer materials transmit sound faster.
These differences have real consequences. Submarines use the speed of sound in water for sonar calculations. Geologists measure seismic wave speeds through rock layers to map underground structures. Engineers account for sound speed in steel when designing ultrasonic testing equipment for inspecting welds and detecting cracks.
Humidity also affects sound speed in air, though less dramatically than temperature. Moist air is slightly less dense than dry air at the same temperature, so sound travels about 0.1 to 0.6% faster in humid conditions. This calculator focuses on temperature as the primary variable since it has the largest effect.
Understanding Mach Numbers
The Mach number expresses speed relative to the local speed of sound. Mach 1 equals the speed of sound, Mach 2 is twice that, and so on. Because the speed of sound changes with temperature and altitude, the same Mach number corresponds to different actual speeds in different conditions.
Below Mach 1 is subsonic flight, the regime where commercial aircraft operate (typically Mach 0.78 to 0.85). Between Mach 0.8 and 1.2 is the transonic regime where shock waves form. Above Mach 1 is supersonic, and above Mach 5 is hypersonic.
The sonic boom heard when an aircraft exceeds Mach 1 occurs because pressure waves pile up into a shock wave. Concorde cruised at Mach 2.04, while the SR-71 Blackbird reached Mach 3.3, the air-breathing aircraft record.
Frequently Asked Questions
How fast does sound travel in air at room temperature?
At 20°C (68°F), the speed of sound in air is approximately 343 m/s (1,125 ft/s or 767 mph). This is the standard reference value used in most physics textbooks and engineering applications.
Why does sound travel faster in water than in air?
Sound travels about 4.3 times faster in water than in air because water molecules are much closer together. Sound is a pressure wave, and denser materials transmit pressure disturbances more quickly. Water's higher density and stiffness both contribute to the roughly 1,482 m/s speed at 20°C.
How does temperature affect the speed of sound?
In air, the speed of sound increases by about 0.6 m/s for each degree Celsius rise in temperature. Warmer air has faster-moving molecules that transmit sound waves more efficiently. The formula v = 331.3 + 0.606T captures this linear relationship, where T is the temperature in Celsius.
What is Mach 1 and does it change?
Mach 1 is the speed of sound in the surrounding air. Since the speed of sound changes with temperature, Mach 1 is not a fixed speed. At sea level and 20°C, Mach 1 is about 343 m/s. At high altitude where temperatures can be -50°C, Mach 1 drops to about 300 m/s. The Mach number is always relative to local conditions.
Why does sound travel fastest in steel?
Steel is extremely rigid, meaning it resists deformation strongly. Sound waves are transmitted through the elastic restoring forces between atoms, and stiffer materials restore faster. Steel's speed of sound is about 5,960 m/s, almost 17 times faster than in air. Aluminum is even faster at 6,420 m/s because it is stiffer relative to its density.