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Notice: The speed of sound changes with the temperature and |
In SI units with dry air at 20 °C (68 °F), the speed of sound c is 343 m/s.
This also equates to 1235 km/h, 767 mph, 1125 ft/s.
Notice: Air density ρ is not the same as air pressure p0.
Statement: Speed of sound - temperature matters, not air pressure
Calculation: Speed of sound c in air and the important temperature
Air Density Calculations
First, consider the ideal gas law:
(1) p × V = n × R × T
| p = pressure, pascals (multiply mb by 100 to get pascals) |
| V = volume in m3 |
| n = number of moles |
| R = gas constant |
| T = temperature K = °C + 273.15 |
Density D = ρ is the number of molecules of the ideal gas in a certain volume.
In this case a molar volume, which can be mathematically expressed as:
(2) D = ρ = n / V
| D = ρ = density in kg/m3 |
| n = number of molecules |
| V = volume in m3 |
By combining the previous two equations, the expression for the density D = ρ becomes:
(3) 
| D = ρ = density in kg/m3 |
| p = pressure, pascals (multiply mb by 100 to get pascals) |
| R = gas constant = 287.05 J / (kg · K) for dry air |
| T = temperature K = °C + 273.15 |
As an example, using the standard sea level conditions of P = 101325 Pa and T = 15 °C,
the air density at sea level, can be calculated as:
D = ρ = 101325 / (287.05 × (15 + 273.15)) = 1.2250 kg/m3
This example has been derived for the dry air of the standard conditions. For real-world situations,
it is necessary to understand how the density is affected by the moisture in the air.
The density D = ρ of a mixture of dry air molecules and water vapor molecules can be expressed as:
(4) 
| D = ρ = density in kg/m3 |
| pd = pressure of dry air in pascals |
| pv = pressure of water vapor in pascals |
| Rd = gas constant for dry air = 287.05 J / (kg · K) |
| Rv = gas constant for water vapor 461.495 J / (kg · K) |
| T = temperature K = °C + 273.15 |
To determine the density of the air, it is necessary to know the actual air pressure,
also known as absolute pressure, or station pressure, the water vapor pressure, and the temperature.
Calculation of the wavelength with frequency and temperature
Speed of sound - temperature matters, not air pressure
Calculation of the wavelength of radio waves and acoustic waves
The speed of sound in water is approximately 1500 m/s. It is possible to measure changes
in ocean temperature by observing the resultant change in speed of sound over long distances.
The speed of sound in an ocean is approximately:
c = 1449.2 + 4.6 × T - 0.055 × T2 + 0.00029 × T3 + (1.34 - 0.01 × T) · (s - 35) + 0.0163 × z
T = temperature in degrees Celsius
s = salinity in parts per thousand
z = depth in meters
Table (chart): The impact of temperature
Speed of sound, density of air, specific acoustic impedance vs. temperature
| Temperature of air °C |
Speed of sound c in m/s |
Time per 1 m Δ t in ms/m |
Density of air ρ in kg/m3 |
Acoustic impedance of air Z in N·s/m3 |
| −25 | 315.7 | 3.165 | 1.423 | 449.7 |
| −20 | 318.9 | 3.134 | 1.395 | 445.1 |
| −15 | 322.0 | 3.103 | 1.368 | 440.9 |
| −10 | 325.2 | 3.073 | 1.341 | 436.5 |
| −5 | 328.2 | 3.044 | 1.316 | 432.4 |
| 0 | 331.3 | 3.017 | 1.293 | 428.3 |
| 5 | 334.3 | 2.990 | 1.269 | 424.5 |
| 10 | 337.3 | 2.963 | 1.247 | 420.7 |
| 15 | 340.3 | 2.937 | 1.225 | 417.0 |
| 20 | 343.3 | 2.912 | 1.204 | 413.5 |
| 25 | 346.2 | 2.888 | 1.184 | 410.0 |
| 30 | 349.1 | 2.864 | 1.164 | 406.6 |
| 35 | 352.0 | 2.840 | 1.146 | 403.5 |
| Sound waves and electromagnetic waves are different. Sound waves need a medium to travel through, while the electromagnetic waves do not. The properties of a sound wave depend on the properties of the medium it travels through. |
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