This calculator estimates the absorption coefficients of multi layer aborbers. Up to four absorbers can be modelled at once, each of which can have up to four layers. It is assumed that there is a rigid backing (such as a solid wall) behind the last layer. The calculator's input parameters are split into three sections:
Global Parameters affect all absorbers. A reset button is provided which returns all global parameters (and parameter options) to their default values.
Parameter Options determine whether certain parameters appear in the Global or Absorber sections. For example, the angle of incidence can be set as a global parameter which affects all absorbers or it can be set to a different value for each absorber.
Absorber Parameters define the absorbers to be modelled. A reset button is provided for each absorber. Each absorber (except the first) also has a copy button which copies all parameters from the absorber directly above.
The parameters in each section are described below:
|Air temperature||The air temperature in degrees Celsius. The default value is 20°C.|
|Air pressure||The air pressure in Pascal. The default value is 101325 Pa.|
|Number of absorbers
to be modelled
|Between 1 and 4 absorbers can be modelled. The default number is 2.|
|Results format||The results can be displayed either as a graph, or as a detailed analysis including information such as surface impedance, angle of propagation, etc.|
|X axis||Where results are to be displayed as a graph, absorption coefficient can be plotted against a number of alternative variables on the X axis. By default, absorption coefficient is plotted against frequency.|
|X range||These fields set the X axis range to be displayed when the results format is set to "Graph".|
|X scale||If the X axis variable is Frequency then the scale can be set to either Logarithmic or Linear. In all other cases the Logarithmic option is disabled.|
|Resolution||The resolution can be set to High, Medium or Low. Higher resolution gives a smoother graph but results in longer calculation times.|
|Frequency||This field sets the frequency at which the analysis is performed. This option is not available if a graph is to be plotted with frequency on the X axis.|
|Random incidence||If this box is checked, the absorption coefficient is calculated for random incidence. This option is not available when the results format is set to "Detailed Analysis" or if a graph is to be plotted with angle of incidence on the X axis.|
|Angle of incidence||The angle of incidence can be set from 0° to 90°, where 0° represents normal incidence. This field is disabled when random incidence is selected and is also not available if a graph is to be plotted with angle of incidence on the X axis.|
|Porous model||This parameter sets which model is used to estimate the properties of porous absorbent layers. The default model is "Allard and Champoux".||Helmholtz model||This parameter sets which model is used to estimate the properties of perforated panels. The default model is "Ingard/Allard".|
|Angle of incidence||When set to "Global", the angle of incidence appears as a global parameter and is applied to all absorbers. When set to "Absorber", the angle of incidence can be set individually for each absorber.|
|Analysis frequency||When set to "Global", the frequency appears as a global parameter and is applied to all absorbers. When set to "Absorber", the frequency can be set individually for each absorber. This option has no effect when the results format is set to "Graph".|
|Porous model||When set to "Global", the model appears as a global parameter and is applied to all absorbers. When set to "Absorber", the model can be set individually for each absorber.|
|Helmholtz model||When set to "Global", the model appears as a global parameter and is applied to all absorbers. When set to "Absorber", the model can be set individually for each absorber.|
This field sets the type of layer as follows:
|Thickness||The thickness of the layer in mm.|
|Flow resistivity||The flow resistivity of the layer in Pa.s/m2 (porous absorbent).|
|Mass||The mass per unit area in Kg/m2 (limp membrane).|
|Hole diameter||The diameter of each hole in mm (perforated panel).|
|Hole spacing||The distance between the holes (centre to centre) in mm (perforated panel).|
|Slot width||The width of each slot in mm (slotted panel).|
|Slot spacing||The distance between the slots (centre to centre) in mm (slotted panel).|
|Random incidence||See global parameters above.|
|Angle of incidence||See global parameters above.|
|Frequency||See global parameters above.|
|Porous model||See global parameters above.|
|Helmholtz model||See global parameters above.|
The formulae used by the calculator have been taken from the following sources:
Trevor J. Cox and Peter D'Antonio. 2009. Acoustic Absorbers and Diffusers: Theory, design and application, 2nd Edition. Taylor & Francis.
F. P. Mechel. 2002. Formulas of Acoustics. Springer.
J. F. Allard and N. Atalla. 2009. Propagation of Sound in Porous Media: Modelling Sound Absorbing Materials, Second Edition. John Wiley & Sons.
M. E. Delany and E.N. Bazley. 1970. Acoustical properties of fibrous absorbent materials. Applied Acoustics, 3, 105-16.
Y. Miki. 1990. Acoustical properties of porous materials - Modification of Delany-Bazley models. J. Acoust. Soc. Jpn., 11, 19-28.
J. F. Allard and Y. Champoux. 1992. New empirical equations for sound propagation in rigid frame fibrous materials. J. Acoust. Soc. Am., 91(6), 3346-53.
T. Komatsu. 2008. Improvement of the Delany-Bazley and Miki models for fibrous sound-absorbing materials. Acoust. Sci. & Tech., 29(2), 121-129.
Note: This calculator makes no attempt to estimate excess absorption at the edges of a finite sample. Random incidence absorption coefficients estimated using the calculator are therefore likely to be lower than those measured in a reverberation chamber.