EN-04Environmental & Occupational Noise
Atmospheric Absorption
ISO 9613-1 air absorption coefficient vs frequency, temperature, humidity and pressure.
Atmosphere
°C
%
kPa
m
Hz
Absorption coefficient
26.6dB/km
Loss over 500 m
13.30dB
Per 100 m
2.66dB
| Band | α dB/km | Loss over 500 m | |
|---|---|---|---|
| 63 Hz | 0.105 | 0.1 dB | |
| 125 Hz | 0.376 | 0.2 dB | |
| 250 Hz | 1.12 | 0.6 dB | |
| 500 Hz | 2.36 | 1.2 dB | |
| 1 kHz | 4.08 | 2.0 dB | |
| 2 kHz | 8.78 | 4.4 dB | |
| 4 kHz | 26.6 | 13.3 dB | |
| 8 kHz | 95 | 47.5 dB | |
| 16 kHz | 331 | 165.7 dB |
§ Theory of operation
Where does the energy go?
Besides spreading geometrically, sound is absorbed by the air itself. Two mechanisms dominate: classicalabsorption (viscosity and heat conduction) which grows with f², and molecular relaxation of oxygen and nitrogen molecules, whose vibrational states lag behind the pressure oscillation and dissipate energy. Water vapour acts as a catalyst for relaxation, so humidity has a strong and non-monotonic effect.
ISO 9613-1 model
\begin{aligned} h &= \mathit{RH} \cdot \dfrac{p_\mathrm{sat}/p_r}{p_a/p_r} \\ f_{rO} &= (p_a/p_r)\,\big(24 + 4.04{\times}10^4\,h\,\tfrac{0.02 + h}{0.391 + h}\big) \\ f_{rN} &= (p_a/p_r)\,(T/T_0)^{-1/2}\,\big(9 + 280\,h\,e^{-4.170\,((T/T_0)^{-1/3} - 1)}\big) \\ \alpha &= 8.686\,f^2\,\Bigl[\, 1.84{\times}10^{-11}\,(p_a/p_r)^{-1}\,(T/T_0)^{1/2} \\ &\qquad + (T/T_0)^{-5/2}\,\Bigl(\, \dfrac{0.01275\,e^{-2239.1/T}}{f_{rO} + f^2/f_{rO}} + \dfrac{0.1068\,e^{-3352/T}}{f_{rN} + f^2/f_{rN}} \,\Bigr) \,\Bigr] \quad \mathrm{dB/m} \end{aligned}
with T_0 = 293.15\ \mathrm{K}, p_r = 101.325\ \mathrm{kPa}, f_{rO} and f_{rN} the relaxation frequencies of oxygen and nitrogen. The standard quotes ±10 % accuracy for 50 Hz–10 kHz, −20–50 °C and 10–100 % RH.
Practical consequences
- Low frequencies travel enormous distances, 63 Hz loses barely 0.1 dB per km, which is why distant thunder, bass at festivals and industrial hum carry so far.
- At 8 kHz absorption can exceed 100 dB/km: over a few hundred metres the high-frequency content of a source vanishes, making distant sounds “dull”.
- Dry, cold air is often more absorbing than humid air at mid frequencies, counter-intuitive but important for winter measurements.
- In large concert halls, air absorption shortens the reverberation time above 2 kHz (the 4mV term in Sabine's formula).