What This Calculator Does
The speed of sound in air depends almost entirely on temperature. This calculator uses the ideal-gas relation \(a = \sqrt{\gamma R T}\) to compute how fast a sound wave travels through air at a given temperature, returning the result in meters per second, kilometers per hour, and miles per hour. It's useful for physics students, acoustics enthusiasts, and engineers estimating sonic conditions.
How to Use It
Enter the air temperature in degrees Celsius. The default adiabatic index \(\gamma = 1.4\) and specific gas constant \(R = 287.05\ \text{J/kg}\cdot\text{K}\) describe dry air, so you can leave those unchanged for most cases. Press calculate to see the resulting speed of sound. Adjust \(\gamma\) and \(R\) if you are modeling a different gas or humid air.
The Formula Explained
Treating air as an ideal gas, sound propagates as an adiabatic compression wave. The wave speed is
$$a = \sqrt{\gamma R T}$$where \(\gamma\) is the ratio of specific heats, \(R\) is the specific gas constant for the gas, and \(T\) is the absolute temperature in kelvin. Because temperature appears under a square root, the speed rises gradually as air warms — roughly 0.6 m/s per degree Celsius near room temperature.
Worked Example
At 20 °C, \(T = 20 + 273.15 = 293.15\ \text{K}\). With \(\gamma = 1.4\) and \(R = 287.05\ \text{J/kg}\cdot\text{K}\):
$$a = \sqrt{1.4 \times 287.05 \times 293.15} = \sqrt{117{,}808} \approx 343.23\ \text{m/s}$$the familiar value for the speed of sound at room temperature.
FAQ
Why does sound travel faster in warm air? Warmer air molecules move faster, transmitting pressure disturbances more quickly, so the wave speed increases with temperature.
Does pressure affect the speed of sound? For an ideal gas, no — pressure cancels out of the equation. Only temperature (and gas composition through \(\gamma\) and \(R\)) matters.
What values should I use for air? Dry air at standard conditions: \(\gamma \approx 1.4\) and \(R \approx 287.05\ \text{J/kg}\cdot\text{K}\). Humid air slightly increases the speed.
