Calculate speed of sound in ideal gases from temperature and properties. Mach number, travel time, and comparison across 10 gases and 15 solids/liquids.
The **Speed of Sound Calculator** computes the speed of sound in ideal gases using v = √(γRT/M), where γ is the heat capacity ratio, R is the universal gas constant, T is absolute temperature, and M is molar mass. It includes 10 common gases, a Mach number analyzer with regime classification, travel time computation, and reference tables of sound speed in 15 solids and liquids.
Sound travels as a longitudinal pressure wave — molecules push against neighboring molecules, transmitting energy through the medium. In air at 20 °C, sound moves at about 343 m/s (1235 km/h). The speed increases with temperature (proportional to √T) and in lighter molecules — helium carries sound nearly three times faster than air, which is why inhaling helium makes your voice sound high-pitched.
The Mach number (object speed / sound speed) determines the flow regime: subsonic (M < 0.8), transonic (0.8–1.2), supersonic (1.2–5), or hypersonic (M > 5). At Mach 1 and above, shock waves form — the "sonic boom" phenomenon. This calculator covers all regimes and shows the Mach angle for supersonic speeds. Sound also travels much faster in solids (steel: 5960 m/s) and liquids (water: 1482 m/s) than in gases.
Understanding sound speed is essential in acoustics, aerodynamics, and atmospheric science. Aircraft designers need precise Mach numbers to predict when shock waves form and how they affect control surfaces. The transonic regime (Mach 0.8–1.2) is particularly challenging because shock waves form on parts of the aircraft while other areas remain subsonic.
Temperature strongly affects sound speed and therefore Mach number. At cruising altitude (−56 °C), the speed of sound drops to about 295 m/s — so a jet at 250 m/s is closer to Mach 1 than it would be at sea level. Pilots must account for this when flying near the sound barrier. Meteorologists use sound speed variations to understand atmospheric stability and acoustic propagation.
Speed of sound in ideal gas: v = √(γRT/M) Simplified for dry air: v ≈ 331.3 × √(T/273.15) m/s Mach number: Ma = v_object / v_sound Mach angle (supersonic): μ = arcsin(1/Ma) Wavelength: λ = v/f Variables: γ = heat capacity ratio (adiabatic index), R = 8.314 J/(mol·K), T = absolute temperature (K), M = molar mass (kg/mol), f = frequency (Hz)
Result: 343.2 m/s speed of sound, Mach 1.98
Air at 20 °C = 293.15 K: v = √(1.4 × 8.314 × 293.15 / 0.02897) = √(118,413) = 343.2 m/s. For an object at 680 m/s: Mach = 680/343.2 = 1.98 (supersonic). Mach angle = arcsin(1/1.98) = 30.3°. Sound travels 1000 m in 2.91 s.
The atmosphere has distinct temperature layers that affect sound propagation. In the troposphere (0–11 km), temperature decreases with altitude, so sound speed drops from ~340 m/s at sea level to ~295 m/s at the tropopause. In the stratosphere (11–50 km), temperature increases due to ozone absorption, causing sound to refract back downward — which is why explosions can sometimes be heard at great distances.
Sound channels form at altitudes where speed is minimum (the "SOFAR" channel in the ocean, or the tropopause in the atmosphere). Sound waves are naturally guided along these channels by refraction, allowing propagation over enormous distances with minimal loss. The ocean SOFAR channel was used during WWII to locate downed pilots by listening for explosive charges.
Breaking the sound barrier creates a sudden increase in aerodynamic drag (the "drag divergence"). Engineers design aircraft with swept wings, area ruling, and thin airfoils to reduce transonic drag. The Concorde cruised at Mach 2.04, while modern fighter jets reach Mach 2.5+. The X-15 research aircraft reached Mach 6.7.
Hypersonic flight (Mach 5+) introduces extreme heating from air compression. At Mach 5, stagnation temperature exceeds 1,500 °C — hot enough to melt aluminum. Thermal protection is the primary challenge for hypersonic vehicles. Scramjet engines, which use supersonic internal airflow, are being developed for propulsion above Mach 5.
Ultrasonic testing uses high-frequency sound waves (1–50 MHz) to inspect materials for internal defects. Medical ultrasound (1–20 MHz) images soft tissues using the reflection of sound at tissue boundaries. Sonar (10 Hz – 1 MHz) maps the ocean floor and detects submarines by measuring sound travel times in water. In all these applications, knowing the precise speed of sound in the medium is essential for accurate distance and position calculations.
Temperature is a measure of molecular kinetic energy. Higher temperature means faster molecular motion, which transmits pressure disturbances more quickly. The speed of sound is proportional to √T (absolute temperature), so doubling the Kelvin temperature increases sound speed by √2 ≈ 41%.
Sound speed v = √(γRT/M). Helium has a lower molar mass (4 g/mol vs 29 g/mol for air) and a higher heat capacity ratio (1.667 vs 1.4). Both factors increase the speed. At 20 °C: helium ≈ 1007 m/s vs air ≈ 343 m/s — almost 3× faster.
When an object exceeds the speed of sound, it creates shock waves that form a cone behind it. The half-angle of this cone is μ = arcsin(1/Mach). When this cone reaches an observer on the ground, they hear a sudden loud "boom." The boom follows the object continuously — it is not just at the moment of breaking the sound barrier.
Sound speed depends on stiffness and density: v = √(E/ρ) for solids. Solids are much stiffer than gases (steel bulk modulus ≈ 160 GPa vs air ≈ 0.14 MPa). Although solids are denser, the stiffness increase far outweighs the density increase, resulting in much higher sound speed.
Yes, slightly. Humid air is less dense than dry air (water vapor M = 18 g/mol replaces N₂ at 28 g/mol), so sound travels slightly faster. At 20 °C, 100% humidity increases speed by about 0.5 m/s compared to dry air — usually negligible except in precision acoustics.
Mach 1 varies with conditions. In air at 20 °C: 343 m/s = 1,235 km/h = 767 mph = 1,125 ft/s. At high altitude (−56 °C): 295 m/s = 1,062 km/h = 660 mph. In water at 20 °C: 1,482 m/s = 5,335 km/h. Always specify the medium and temperature with Mach numbers.