Formula for calculating the damping of air

 ISO 9613-1:1993 − Acoustics − Noise Absorption by Air − Attenuation of sound during propagation outdoors − Calculation of the absorption of sound by the atmosphere. Dämpfung durch atmosphärische Absorption wird als Funktion der Frequenz des Schalls von 50 Hz bis 10 kHz angegeben und das ist wirklich kein Ultraschall.   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. 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