Pressure drops out
At fixed temperature and composition, ideal-gas sound speed ignores pressure. Thin air is not slower if it is the same temperature.
Ideal-gas magic
Speed of Sound in Air vs Temperature Calculator
Quick Answer
At 20°C / 68°F, the speed of sound in dry air is about 343 m/s, 1,235 km/h, 767 mph, or 1,125 ft/s.
A useful formula near room temperature is \( c \approx 331.3 + 0.606T_{^\circ\!C} \) m/s.
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How the Speed of Sound Depends on Temperature (and Humidity)
For an ideal gas, the speed of sound is \( c = \sqrt{\gamma R T} \) where \( \gamma \) is the heat-capacity ratio, \( R \) is the specific gas constant of the mixture, and \( T \) is absolute temperature in kelvins. Near room temperature in dry air, a handy approximation is the linear rule \( c \approx 331.3 + 0.606\,T_{^\circ\!C} \) m/s.
Humidity slightly increases \( c \) because water vapor has a larger \( R \) than dry air and a different heat capacity. This tool can estimate the moist-air effect by computing vapor pressure from temperature and relative humidity, then mixing dry air and water vapor properties to obtain an effective \( R \) and \( \gamma \). Pressure mainly constrains how much vapor the air can hold; with composition fixed, \( c \) is pressure-independent in the ideal-gas model.
Rule of thumb: changing from 0% to ~50% RH at 20 °C nudges \( c \) up by roughly 0.5–1%. For most everyday acoustics, the linear formula is fine; use the moist model for measurement work or when precision matters.
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Speed of Sound in Air Temperature Table
| Temperature | Speed of sound |
|---|---|
| -40°C | 306.2 m/s |
| 0°C | 331.4 m/s |
| 10°C | 337.4 m/s |
| 20°C | 343.3 m/s |
| 25°C | 346.3 m/s |
| 30°C | 349.1 m/s |
| 40°C | 354.7 m/s |
These dry-air reference values are close to the calculator's linear estimate near ordinary weather temperatures. Humidity and gas composition can shift the result slightly.
Speed of Sound in Air — Deep Dive (Temperature, Humidity, and More)
The speed of sound describes how fast small pressure disturbances travel through a medium. For an ideal gas such as air, the fundamental relation is \( c = \sqrt{\gamma\,R\,T} \), where \( \gamma \) is the ratio of heat capacities \( c_p/c_v \), \( R \) is the specific gas constant of the gas mixture, and \( T \) is the absolute temperature in kelvins. This reveals the key dependence: sound gets faster as temperature rises (since \( c \propto \sqrt{T} \)).
Dry-Air Rule of Thumb
Near room temperature, a widely used linear approximation is \( c \approx 331.3 + 0.606\,T_{^\circ\!C} \) m/s. At \(20^\circ\)C this gives about 343 m/s, which matches everyday experience and many classroom measurements. The linear form is simply a convenient fit to the square-root law over a limited range.
Why Humidity Matters (A Little)
Real air contains water vapour. Replacing some dry air with water vapour changes the mixture’s properties: the gas constant increases (water vapour has a larger \( R \)) and the effective heat capacity changes, nudging \( \gamma \) and \( R \) in the formula. The net effect is that humid air carries sound slightly faster than completely dry air at the same temperature and pressure. The change is modest (typically ~0.5–1% from 0% to 50% RH at 20 °C), but it can matter for careful measurements, time-of-flight sensing, and microphone calibration.
Pressure, Altitude, and Composition
In the ideal-gas view, if the gas composition is fixed, sound speed does not explicitly depend on pressure. That’s why at the same temperature, sea-level and mountain-top air have nearly the same \( c \) despite very different densities. However, altitude often goes hand-in-hand with lower temperatures, and it is the temperature drop that reduces \( c \). Long-term composition shifts (e.g., CO\(_2\) fraction) or trace gases also tweak \( R \) and \( \gamma \), though the effect on \( c \) is small in typical atmospheres.
Worked Example
Suppose \( T = 25^\circ\mathrm{C} \) (298.15 K), 50% RH, and 101.325 kPa. A moist-air model blends dry-air and water-vapour properties to estimate \( R_\text{mix} \) and \( \gamma \). Plugging them into \( c = \sqrt{\gamma\,R_\text{mix}\,T} \) yields a value a little above the dry-air linear estimate \( 331.3 + 0.606\times25 \approx 346.45 \) m/s. The difference—fractions of a percent—illustrates humidity’s subtle but measurable role.
From Speed to Wavelength and Mach
Once you know \( c \), you can compute wavelength at frequency \( f \) via \( \lambda = c/f \) (e.g., at 1 kHz and \( c=343 \) m/s, \( \lambda \approx 0.343 \) m). In aerodynamics and audio measurements, Mach number is \( \mathrm{Ma} = v/c \); because \( c \) tracks temperature, the same vehicle speed may correspond to different Mach numbers on a hot runway versus a cold morning.
Common Pitfalls
- Mixing units: Always convert to kelvins before using the square-root formula.
- Over-extending the linear fit: The \(331.3+0.606T\) rule is great near room temperature, less accurate far from it.
- Ignoring humidity in precision work: For time-of-flight sensors or long baselines, include RH (and temperature gradients).
- Confusing density with speed: In ideal gases, higher density does not automatically mean slower sound; temperature and composition are what matter.
This tool offers both the simple linear estimate and a moist-air model using relative humidity and pressure. For metrology-grade results (wide temperature ranges, high humidity, or unusual gas mixes), use full thermodynamic property libraries and consider temperature stratification along the path.
5 Fun Facts about Sound and Temperature
Humidity speeds things up
Water vapor is lighter than dry air, so humid air carries sound slightly faster. The effect is small but measurable.
Moist boost
Mach 1 is a moving target
Because speed depends on temperature, the Mach 1 number is higher on a hot runway than on a cold morning.
Speed of sound is not constant
Square-root rule
Sound speed scales with the square root of absolute temperature, so big temperature swings change it less than you might guess.
Gentle curve
Wavelength shifts with heat
At a fixed frequency, a warmer day makes sound speed higher, so the wavelength gets longer too.
Longer waves
Speed of Sound in Air FAQ
What is the speed of sound at 20°C?
At 20°C or 68°F, the speed of sound in dry air is about 343 m/s, 1,235 km/h, 767 mph, or 1,125 ft/s.
What is the formula for speed of sound in air?
A useful dry-air approximation near room temperature is \( c \approx 331.3 + 0.606T_{^\circ\!C} \) m/s. The ideal-gas relation is \( c = \sqrt{\gamma R T} \), where \( T \) is absolute temperature.
Does humidity change the speed of sound?
Yes. Humid air carries sound slightly faster than dry air at the same temperature because water vapor changes the gas mixture properties. The effect is usually small, often less than about 1% near room temperature.
Does pressure affect the speed of sound?
For an ideal gas at fixed temperature and composition, pressure does not directly change the speed of sound. Pressure can still matter indirectly because it affects density, altitude conditions, and how much water vapor air can contain.
Why does sound travel faster in warm air?
Warm air has a higher absolute temperature, so molecular motion and pressure disturbances propagate faster. In ideal gases, sound speed scales with the square root of absolute temperature.
What is Mach 1 at room temperature?
At about 20°C, Mach 1 in dry air is roughly 343 m/s, 1,235 km/h, 767 mph, or 1,125 ft/s. Mach 1 changes with air temperature.
Is the speed of sound constant?
No. The speed of sound depends on the medium. In air it changes mainly with temperature, and slightly with humidity and gas composition.
Sources and References
- U.S. Standard Atmosphere, 1976 for standard dry-air atmosphere properties and the speed-of-sound relation.
- Engineering ToolBox air speed vs temperature reference table for dry-air temperature reference values.
- National Weather Service speed of sound calculator for a practical temperature-based calculator reference.
- Fundamental ideal-gas relation: \( c = \sqrt{\gamma R T} \).