Calculation of the damping of air formula atmosphere acoustics noise absorption by air attenuation of sound air damping

● Formula for calculating the damping of air ●

Damping of Air of High Frequencies (Dissipation)

ISO 9613-1:1993 − Acoustics − Noise Absorption by Air − Attenuation of sound during propagation outdoors − Calculation of the absorption of sound by the atmosphere.
Attenuation due to atmospheric absorption is specified as a function of the frequency of the sound from 50 Hz to 10 kHz and that is really no ultrasound.

There are 4 parameters for calculating air damping:
1) Frequency f in Hz
2) Temperature T in K (Kelvin). Can be fixed to a standard room temperature of 293.15 K
= 20°C = 68°F
3) Relative Humidity h in %. Can be fixed to a standard of 50 to 60% or whatever represents a standard RH for one's circumstances.
4) Atmospheric pressure p in kPa (kilopascal). Can be fixed to a standard of 101.325 kPa (standard pressure at sea level).

as = a · s [dB] total absorption at distance s

pt = pi · exp(−x · as) [Pa]
x = 1 / (10 · log ((exp(1))²) = ca. 0.1151
Delta Lt = 20 · log (pi / pt) = as [dB]
a = 8.686 · f² · ((1.84 · 10⁻¹¹ · (pa / pr)⁻¹ · (T / To)^1/2) + y) [dB/m]
y = (T / To)^−5/2· (0.01275 · exp (−2239.1 / T) · (frO + f² / frO)⁻¹ + z)
z = 0.1068 · exp (−3352 / T) · (frN + f² / frN)⁻¹
frO = (pa / pr) · (24 + 4.04 · 10⁴ · h · ((0.02 + h) / (0.391 + h)))
frN = (pa / pr) · (T / To)^−1/2 · (9 + 280 · h · exp (−4.170 · ((T / To)^−1/3−1)))
h = hr · ((psat / pr) / (pa / pr)) = hr · (psat / pa)
psat = pr · 10^{(−6.8346 · (To1 / T)^{^1.261} + 4.6151)}

a ........ pure-tone sound attenuation coefficient, in dB/m, for atmospheric absorption
s ........ distance in m through which the sounds propagates
pi ....... initial sound pressure amplitude in Pa
pt ....... sound pressure amplitude in Pa
pa ...... ambient atmospheric pressure in kPa
pr ....... reference ambient atmospheric pressure: 101.325 kPa
psat ... saturation vapor pressure equals:
................ International Meteorological Tables WMO-No.188 TP94
................ World Meteorological Organization - Geneva Switzerland
T ........ ambient atmospheric temperature in K (Kelvin).
........... K = 273.15 + Temperature in °C (Celsius)
To ...... reference temperature in K: 293.15 K (20°C)
To1..... triple-point isotherm temp: 273.16 K = 273.15 + 0.01 K (0.01°C)
h ........ molar concentration of water vapor, as a percentage
hr........ relative humidity as a percentage
f ......... frequency
frO ..... oxygen relaxation frequency
frN ..... nitrogen relaxation frequency
x ........ a help factor to shorten formula − improvement by E. Desart
y ........ a help factor to shorten formula
z ........ a help factor to shorten formula

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