RACK/PROPAGATION & AIR
αair\alpha_{air}

Air HF Absorption

Frequency-dependent air loss over distance (ISO 9613-1) from temperature and humidity.

MOD-03•ISO 9613-1 ATMOSPHERIC ATTENUATION MODEL

Atmospheric HF Air Absorption Calculator

Calculate frequency-dependent high-frequency dissipation caused by Oxygen (O2\text{O}_2) and Nitrogen (N2\text{N}_2) molecular relaxation across long throw distances.

Climate Presets
AIR LOSS @ 8.0 kHz (60m)ΔLair\Delta L_{\text{air}}
−9.9dB
4 kHz: −2.8 dB12 kHz: −19.3 dB
ABSORPTION COEFFICIENTα(f)\alpha(f)
16.45dB / 100m
0.165 dB/mISO 9613-1 Standard
SAFE DSP HF SHELF COMPENSATIONGEQG_{\text{EQ}}
+7.4dB
75% Recovery TargetMax Safe Cap: +12 dB
METEOROLOGICAL & THROW PARAMETERS
m
10 m150 m
°C
-5 °C45 °C
%
10 %95 %
kPa
82 kPa106 kPa
Hz
500 Hz18000 Hz
HF FREQUENCY RESPONSE ROLL-OFF & DSP COMPENSATION (100Hz – 20kHz)
Air Roll-Off @ 25°C, 25% RHDSP Air-Comp EQ CurveRef (20°C / 60% RH)
+10dB0dB-10dB-20dB-30dB1002505001k2k4k8k16k−9.9dB @ 8.0kHz
Counter-Intuitive Physics: Dry air (15% RH) absorbs MORE HF than humid air (70% RH)!Throw: 60m
HOW IT WORKS: ELECTRO-ACOUSTIC PHYSICS & MATHEMATICAL DERIVATION

ISO 9613-1 Molecular Relaxation Physics (O₂ & N₂)

When acoustic waves propagate through the atmosphere, high-frequency energy is dissipated into heat via two mechanisms: classical viscosity/thermal conduction and molecular vibrational relaxation of diatomic Oxygen (O2\text{O}_2) and Nitrogen (N2\text{N}_2) molecules. Water vapor (H2O\text{H}_2\text{O}) acts as a catalytic lubricant for these vibrational transitions, shifting the relaxation frequencies frOf_{rO} and frNf_{rN} upward.

Because of this molecular catalysis, arid desert conditions (10%–20% RH10\%\text{–}20\%\text{ RH}) place the oxygen relaxation peak directly inside the audible upper-treble band (4 kHz–12 kHz4\text{ kHz–}12\text{ kHz}), causing severe high-frequency loss! Increasing relative humidity to 60%–80%60\%\text{–}80\% pushes the relaxation frequency well above 20 kHz20\text{ kHz}, significantly reducing audible air loss.

ISO 9613-1 Attenuation Coefficient (dB / meter)EQ-01
α(f)=8.686⋅f2(1.84×10−11T/T0pa/pr+(TT0)−5/2[0.01275 e−2239.1/TfrO+f2/frO+0.1068 e−3352/TfrN+f2/frN])\alpha(f) = 8.686 \cdot f^2 \left( 1.84\times 10^{-11} \frac{\sqrt{T/T_0}}{p_a/p_r} + \left(\frac{T}{T_0}\right)^{-5/2} \left[ \frac{0.01275\,e^{-2239.1/T}}{f_{rO} + f^2/f_{rO}} + \frac{0.1068\,e^{-3352/T}}{f_{rN} + f^2/f_{rN}} \right] \right)
Total High-Frequency Roll-Off at Distance dEQ-02
ΔLair(f,d)=−α(f)⋅d[dB]\Delta L_{\text{air}}(f, d) = -\alpha(f) \cdot d \quad [\text{dB}]

Nomenclature & Physical Variables

  • α(f)\alpha(f)
    Pure-tone atmospheric sound absorption coefficient
    Unit: dB/m
  • frO,frNf_{rO}, f_{rN}
    Vibrational relaxation frequencies of Oxygen and Nitrogen
    Unit: Hz
  • RHRH
    Relative Humidity of ambient air
    Unit: %
  • pap_a
    Ambient barometric atmospheric pressure
    Unit: kPa
FOH & System Tech Field Application Notes
  • Zone your line array into Long-Throw (top boxes), Mid-Throw, and Near-Field (bottom boxes) DSP groups. Apply progressive ISO 9613-1 HF air-compensation shelving only to the upper long-throw cabinets so front-row listeners are not blasted with harsh treble.
  • Never attempt to compensate 100%100\% of air loss above 12 kHz12\text{ kHz} at 80 m+80\text{ m+}; cap HF boost around +9 dB+9\text{ dB} to +12 dB+12\text{ dB} to protect compression driver diaphragms.