Speed of Sound Calculator
Calculate the speed of sound in air, water, or steel based on temperature. For air, uses the formula v = 331.3 + 0.606×T (°C). Also shows Mach number reference and wavelength calculations. See also our Frequency Calculator and Doppler Effect Calculator.
How to Calculate Speed of Sound
The speed of sound is the rate at which sound waves propagate through a medium. Unlike light, sound requires a material medium (solid, liquid, or gas) to travel — it cannot propagate through a vacuum. The speed depends on the medium's properties: its elasticity (how easily it springs back when compressed) and its density (how much mass per unit volume). Stiffer, less dense materials generally transmit sound faster.
In air, the speed of sound depends primarily on temperature. The simplified formula v = 331.3 + 0.606×T gives the speed in m/s for temperature T in degrees Celsius. At 20°C, sound travels at about 343 m/s (1,235 km/h or 767 mph). The temperature dependence arises because warmer air molecules move faster and transmit pressure waves more quickly. Humidity has a small effect (moist air is slightly faster), and pressure has negligible effect at normal conditions.
Sound travels much faster in liquids and solids than in gases. In water, sound travels at about 1,480 m/s — over 4 times faster than in air. In steel, it reaches about 5,960 m/s — over 17 times faster than in air. This is because solids and liquids are much stiffer (higher bulk modulus) than gases, and although they are denser, the stiffness effect dominates. This is why you can hear a train approaching by putting your ear to the rail long before you hear it through the air.
The Mach number is the ratio of an object's speed to the local speed of sound: M = v_object / v_sound. Mach 1 is the speed of sound (sonic), below Mach 1 is subsonic, and above is supersonic. When an object exceeds Mach 1, it creates a shock wave (sonic boom). The speed of sound varies with altitude because temperature decreases with height — at 11 km altitude (typical cruising altitude), the speed of sound is only about 295 m/s due to the -56°C temperature.
Speed of Sound Formula
In air (simplified):
v = 331.3 + 0.606 × T (°C)
In air (exact):
v = 331.3 × √(1 + T/273.15)
General formula (ideal gas):
v = √(γRT/M)
γ = adiabatic index, R = gas constant
T = absolute temperature (K), M = molar mass
In solids:
v = √(E/ρ) (thin rod)
E = Young's modulus, ρ = density
In liquids:
v = √(K/ρ)
K = bulk modulus, ρ = density
Mach number:
M = v_object / v_sound
Example Calculation
Calculate the speed of sound in air at 20°C and determine how far sound travels in 3 seconds:
Given: T = 20°C
v = 331.3 + 0.606 × 20 = 331.3 + 12.12 = 343.42 m/s
Distance in 3 seconds: d = v×t = 343.42 × 3 = 1030.3 m ≈ 1.03 km
Lightning flash rule: count seconds between flash and thunder
Distance (km) ≈ seconds / 3
Distance (miles) ≈ seconds / 5
At cruising altitude (-56°C):
v = 331.3 + 0.606×(-56) = 331.3 - 33.9 = 297.4 m/s
Mach 1 at altitude = 297.4 m/s = 1071 km/h
Speed of Sound Reference Table
| Medium | Speed (m/s) | Ratio to Air |
|---|---|---|
| Air (0°C) | 331.3 m/s | 1.0× |
| Air (20°C) | 343.2 m/s | 1.0× |
| Air (40°C) | 355.5 m/s | 1.1× |
| Helium (20°C) | 1007 m/s | 2.9× |
| Fresh water (20°C) | 1480 m/s | 4.3× |
| Seawater (20°C) | 1522 m/s | 4.4× |
| Rubber | 1600 m/s | 4.7× |
| Concrete | 3400 m/s | 9.9× |
| Glass | 5640 m/s | 16.4× |
| Steel | 5960 m/s | 17.4× |
| Aluminum | 6420 m/s | 18.7× |
| Diamond | 12000 m/s | 35.0× |
Frequently Asked Questions
Why does temperature affect the speed of sound?
Temperature affects the speed of sound because it determines how fast air molecules move. Sound propagates through collisions between molecules — faster-moving molecules (higher temperature) transmit these collisions more quickly. Mathematically, v ∝ √T (absolute temperature). A 1°C increase raises the speed by about 0.6 m/s. This is why sound travels faster on hot days. At -40°C, sound speed is only 306 m/s; at +40°C, it reaches 355 m/s — a significant difference for acoustic calculations.
Why is sound faster in solids than gases?
Sound speed depends on the ratio of stiffness to density: v = √(modulus/density). Solids are much stiffer than gases (steel's Young's modulus is ~200 GPa vs air's bulk modulus of ~140 kPa — a million times stiffer). Although solids are also much denser, the stiffness advantage overwhelms the density penalty. The atoms in a solid are tightly bonded and transmit vibrations almost instantly to neighbors. In a gas, molecules must physically travel to collide with neighbors, which is much slower.
What is a sonic boom?
A sonic boom occurs when an object travels faster than sound (supersonic, Mach > 1). The object outruns its own pressure waves, which pile up into a cone-shaped shock wave (Mach cone). When this shock wave passes an observer, they hear a loud "boom." The boom is continuous as long as the object is supersonic — it's not just at the moment of "breaking the sound barrier." The Concorde produced sonic booms that could be heard 40 km away. The half-angle of the Mach cone is sin(θ) = 1/M.
Does humidity affect the speed of sound?
Yes, but the effect is small. Humid air is slightly less dense than dry air (water vapor, molecular weight 18, replaces nitrogen/oxygen, molecular weight 28-32), so sound travels slightly faster in humid air. At 20°C, going from 0% to 100% relative humidity increases the speed by about 1.5 m/s (from 343.2 to 344.7 m/s). This is usually negligible for practical purposes but matters in precision acoustic measurements and musical instrument tuning.
How is the speed of sound measured?
Several methods exist: (1) Direct timing — measure the time for sound to travel a known distance (echo method). (2) Resonance tube — find resonant frequencies in a tube of known length; v = f×λ where λ relates to tube length. (3) Kundt's tube — standing waves in a tube create visible patterns in powder, revealing wavelength directly. (4) Interferometry — compare phases of sound waves traveling different paths. Modern measurements use electronic timing with microsecond precision, achieving accuracy better than 0.1 m/s.
What is the speed of sound in space?
Sound cannot travel through the vacuum of space — there are no molecules to transmit pressure waves. However, in interstellar gas clouds (very low density), sound can technically propagate, though at very low frequencies (periods of thousands of years). In 2022, NASA released a "sonification" of a black hole, but this was data converted to sound, not actual sound waves. Inside stars, sound waves do propagate — helioseismology studies the Sun's interior using sound wave patterns on its surface.
Applications of Speed of Sound
The speed of sound has numerous practical applications. Sonar (Sound Navigation and Ranging) uses sound speed in water to measure ocean depth and detect submarines. Ultrasonic distance sensors measure the time for sound echoes to return. Thunder-lightning timing estimates storm distance. Acoustic thermometry measures temperature by measuring sound speed. In medicine, ultrasound imaging relies on knowing sound speed in tissue (~1540 m/s) to calculate distances from echo timing.
In aerospace, the speed of sound determines aircraft design constraints. Transonic flight (Mach 0.8-1.2) creates complex shock wave patterns requiring careful aerodynamic design. Supersonic aircraft (Concorde, military jets) must manage heating from air compression and the sonic boom footprint. Hypersonic vehicles (Mach 5+) face extreme heating challenges. Even subsonic aircraft are affected — the critical Mach number determines the maximum efficient cruise speed before drag rises sharply due to local supersonic flow over the wings.