Ambient air temperature

material.ambient.temperature_C Unit: °C Step 04 · Material

The temperature of the air outside the muffler, in the Material step's Ambient air panel together with the atmospheric pressure and the relative humidity. It is used twice: the outlets radiate into this air (insertion loss, Insertion loss: radiation into the ambient air), and it sets the atmospheric attenuation coefficient $\alpha$ of the radiated SPL's path from the outlet to the microphone (ISO 9613-1). It is not the gas temperature inside the muffler (Temperature).

Last updated 2026-11-11

Theory

Sound in air is absorbed by two mechanisms:

viscosity and heat conduction (classical and rotational absorption);
vibrational relaxation of oxygen and nitrogen molecules, whose relaxation frequencies depend on the water-vapour content and the temperature.

The program computes the pure-tone attenuation coefficient of ISO 9613-1, equation (1), with the relaxation frequencies of equations (2) and (3). At the default distance of 0.5 m the absorption is small (hundredths of a dB at a few kHz); it becomes significant at large distances and high frequencies.

Equations

\alpha = 8.686 f^2\left[1.84\times10^{-11}\left(\frac{p_a}{p_r}\right)^{-1}\left(\frac{T}{T_0}\right)^{1/2} + \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^{-3352.0/T}}{f_{rN} + f^2/f_{rN}}\right)\right]

(1)

f_{rO} = \frac{p_a}{p_r}\left(24 + 4.04\times10^{4}\,h\,\frac{0.02 + h}{0.391 + h}\right)

(2)

f_{rN} = \frac{p_a}{p_r}\left(\frac{T}{T_0}\right)^{-1/2}\left(9 + 280\,h\,\exp\!\left[-4.170\left(\left(\frac{T}{T_0}\right)^{-1/3} - 1\right)\right]\right)

(3)

where	meaning	unit
$\alpha$	Attenuation coefficient	dB/m
$f$	Frequency	Hz
$p_a$	Ambient pressure	kPa
$p_r$	Reference pressure, 101.325	kPa
$T$	Air temperature (this setting, in kelvin)	K
$T_0$	Reference temperature, 293.15	K
$f_{rO}, f_{rN}$	Relaxation frequencies of oxygen and nitrogen	Hz
$h$	Molar concentration of water vapour (Relative humidity)	%

Default and rule

Default: 25 °CMeasured
Rule: 25 °C.
Source: The equations are those of ISO 9613-1, eqs. (3)-(5). The implementation was verified against a tabulation of the attenuation coefficients (relative humidity 10-100 %, the temperatures of the input range, the tabulated frequencies): 1789 of 1848 values agree within 0.5 % (median 0.07 %). The remaining 59 differ because of transcription errors in the tabulation (decade or digit errors, e.g. 0.897 where 0.0897 is correct at 20 °C / 63 Hz / 70 %). The input range 15-40 °C is the program's.

Valid range -40 to 60 °C (radiated SPL: 15 to 40 °C)

Values

-40 to 60 °C, the range of the insertion loss's outside air.

Radiated SPL

The radiated SPL accepts 15 to 40 °C only: a run that computes it is refused outside that range.

Theory

Equations

Default and rule

Valid range -40 to 60 °C (radiated SPL: 15 to 40 °C)

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