Speed of Sound Calculator
Calculate the speed of sound in dry air using c = sqrt(γRT) at any temperature. Free online physics calculator with results in m/s, km/h, ft/s, mph, and knots.
About This Calculator
The Speed of Sound Calculator computes the velocity of sound waves propagating through dry air at any given temperature. This free online tool is essential for students of physics and acoustics, pilots and aviation professionals, audio engineers, meteorologists, and anyone working with sound propagation. The calculator uses the fundamental physics formula for the speed of sound in ideal gases and presents results in five common units: meters per second (m/s), kilometers per hour (km/h), feet per second (ft/s), miles per hour (mph), and knots.
How the Speed of Sound Is Calculated
The speed of sound in dry air is derived from the ideal gas law and the adiabatic relationship for compressible fluids. The formula is c = √(γRT), where γ (gamma) is the adiabatic index (ratio of specific heats Cp/Cv), which equals 1.4 for dry air, R is the specific gas constant for dry air (287.058 J/kg·K), and T is the absolute temperature in Kelvin. The simplified form, c = 331.3 × √(1 + T/273.15) where T is in °C, gives the speed in m/s. At 20°C, the speed of sound is approximately 343 m/s.
Factors Affecting the Speed of Sound
Temperature is the primary factor affecting the speed of sound in air. Sound travels faster in warmer air because molecules move more rapidly, transmitting vibrational energy more quickly. Unlike common misconceptions, air pressure and density at a given temperature do not affect sound speed — the formula depends only on temperature. Humidity has a minor effect (moist air is slightly less dense, increasing speed by less than 1%), and wind can affect the effective speed relative to a ground observer.
Frequently Asked Questions
How does temperature affect the speed of sound?
The speed of sound increases as air temperature increases because air molecules move faster at higher temperatures, transmitting sound waves more quickly. The speed of sound at 20°C is about 343 m/s, while at 0°C it is about 331 m/s. The relationship follows the formula c = sqrt(γRT), where T is the absolute temperature in Kelvin.
What is the formula for the speed of sound in air?
The speed of sound in dry air is calculated using c = sqrt(γ × R × T), where γ (gamma) is the adiabatic index (1.4 for air), R is the specific gas constant for dry air (287.058 J/kg·K), and T is the absolute temperature in Kelvin. The simplified formula is c = 331.3 × sqrt(1 + T/273.15) where T is in °C.
What is the speed of sound at room temperature?
At room temperature (20°C or 68°F), the speed of sound in dry air is approximately 343 m/s or 767.6 mph. This is the standard value commonly used in acoustics, aviation, and physics calculations.
Does humidity affect the speed of sound?
Yes, humidity has a small effect on the speed of sound. Moist air is less dense than dry air, so sound travels slightly faster in humid air. However, the effect is very small — typically less than 1% change — and temperature is by far the dominant factor.
How fast does sound travel in water compared to air?
Sound travels much faster in water than in air. At 20°C, the speed of sound in water is approximately 1,482 m/s, compared to just 343 m/s in air. This is because water is much denser and has a higher bulk modulus, allowing sound waves to propagate more efficiently.
Can sound travel in a vacuum?
No, sound cannot travel in a vacuum because sound waves require a medium (solid, liquid, or gas) to propagate. Sound travels by causing molecules to vibrate and pass energy to neighboring molecules — with no molecules, there is no transmission.
Why does sound travel faster at higher altitudes even though it is colder?
Sound speed depends on temperature, not air pressure. However, at higher altitudes, the temperature decreases in the troposphere, so sound actually travels slower, not faster. The common misconception may arise because aircraft travel faster at altitude due to reduced drag, but the speed of sound itself decreases with altitude in the troposphere.
What is Mach number and how does it relate to the speed of sound?
Mach number is the ratio of an object's speed to the speed of sound in the surrounding medium. Mach 1 equals the speed of sound. When an aircraft exceeds Mach 1, it breaks the sound barrier, creating a sonic boom. At sea level and 15°C, Mach 1 is approximately 340 m/s or 1,225 km/h.