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Calculation: speed of sound in humid air

This calculation shows the speed of sound in humid air according to Owen Cramer, "JASA, 93, p. 2510, 1993", with saturation
vapor pressure taken from Richard S. Davis, "Metrologia, 29, p. 67, 1992", and a mole fraction of carbon dioxide of 0.0004.
The calculator is valid over the temperature range 0 to 30° C (273.15 - 303.15 K) and over the pressure range 75 to 102 kPa.
In the region between the air pressures 95.000 und 104.000 kPa there is no noticeable changing of the speed of sound.

Temperature   °Celsius
Air pressure   kPa
 Relative humidity   %
   
Speed of sound   m/s

Notice: The speed of sound changes with the temperature and
               a little bit with the humidity, but not with our air pressure.

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

Impedance of Air, Density of Air, and Speed of Sound
in Dependance of the Temperature

Temperature
θ in °C
Speed of sound
c in m/s
Density
ρ in kg/m³
Impedance of air
ZF in Ns/m³
-10 325.4 1.341 436.5
-5 328.5 1.316 432.4
0 331.5 1.293 428.3
5 334.5 1.269 424.5
10 337.5 1.247 420.7
15 340.5 1.225 417.0
20 343.4 1.204 413.5
25 346.3 1.184 410.0
30 349.2 1.164 406.6

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