Conversion between Air Permeability and Specific Acoustic Resistance

Some manufacturers do not specify Specific Acoustic Impedance in the material's data sheet, but do give a value for Air Permeability. This is measured with a continuous airflow and not with sound. The Air Permeability can be converted to a Specific Acoustic Resistance with the equations stated below.

Please note:

• If the material is capacitive or membrane-like, the dominant element of the acoustic impedance is equivalent to a capacitor in series. Air Permeability describes the equivalent of a leakage resistor which is placed in parallel. It does not say anything about the capacitive behavior.
• For resistive materials, the resistive element is all there is. In this case, Specific Acoustic Resistance and Specific Acoustic Impedance are the same.
• The equations assume laminar airflow, which might not be the case for very open materials. Do not use these equations for air permeabilities above 12,000 $\frac{\mathrm{ml}}{\mathrm{c}{\mathrm{m}}^2\cdot \min }$ @ 70 mbar resp. 2,000 $\frac{\mathrm{L}}{{\mathrm{m}}^2\cdot \mathrm{s}}$ @ 20 mmWG.

Conversion when air permeability is given in ml/(cm² $\cdot$ min) at 70 mbar to Rayl

In some specifications, the air permeability is given in units of ($\frac{\mathrm{ml}}{\mathrm{c}{\mathrm{m}}^2\cdot \min }$) at a pressure difference of 70 mbar. Here we provide the conversion factor to convert the air permeability to more standard units used in acoustics.

$$r_s=\frac{C_1}{q_{70mbar}}$$

in which:

• $r_s$ is the specific acoustic resistance (MKS Rayl = $\frac{\mathrm{Pa}\cdot \mathrm{s}}{\mathrm{m}}$)

• $q_{70mbar}$ is the air permeability in units of ($\frac{\mathrm{ml}}{\mathrm{c}{\mathrm{m}}^2\cdot \min }$) at a pressure difference of 70 mbar

• $C_1=4.2\cdot 10^7$ is a constant ($\frac{\mathrm{Pa}}{70mbar}\cdot \frac{\mathrm{s}}{\min }\cdot \frac{\mathrm{ml}}{\mathrm{m}\cdot \mathrm{c}{\mathrm{m}}^2}$).

Conversion when air permeability is given in L/(m² $\cdot$ s) at 20 mmWG to Rayl

$$r_s=\frac{C_2}{q_{20mmWG}}$$

in which:

• $r_s$ is the specific acoustic resistance (MKS Rayl = $\frac{\mathrm{Pa}\cdot \mathrm{s}}{\mathrm{m}}$)

• $q_{20mmWG}$ is the air permeability in units of ($\frac{\mathrm{L}}{{\mathrm{m}}^2\cdot \mathrm{s}}$ at a pressure difference of 20 mmWG

• $C_2=1.96\cdot 10^5$ is a constant ($\frac{\mathrm{Pa}}{20mmWG}\cdot \frac{\mathrm{L}}{{\mathrm{m}}^3}$).