The Impedance node adds an impedance boundary condition with the option to select between several built-in impedance models and engineering relations. The impedance condition is a generalization of the sound hard and sound soft boundary conditions:

Here, Zn is the (normal) specific impedance of the external domain and it has the SI unit Pa·s/m — a pressure divided by a velocity. From a physical point of view, the acoustic input impedance is the ratio between the local pressure and local normal particle velocity. The Impedance boundary condition is a good approximation of a locally reacting surface — a surface for which the normal velocity at any point depends only on the pressure at that exact point.

For plane waves, the specific impedance Zn is related to the acoustic impedance Zac (ratio of average surface pressure and flow rate) and the mechanical impedance Zmech (ratio of force and velocity) via the area A of the boundary, according to

In the frequency domain, the impedance can be any complex-valued number or function and thus models a surface that is both resistive and reactive. In the time domain the same resistive and reactive effects can be included in the Impedance (time domain). In the time domain the approach is based on the so-called partial fraction approximation to the frequency dependent data.

Choose an Impedance model — User defined (the default), RCL, Physiological, Waveguide end impedance, Porous layer, Specific characteristic impedance, or Absorption Coefficient.

Allows the user to enter any expression and is the only impedance model that applies to time-dependent models. It is advantageous to enter complicated user-defined models as a variable under the Definitions node or use an interpolation function for measured data.

Enter the value of the Specific impedance Zn (SI unit: Pa·s/m). The default value is set to the characteristic specific acoustic impedance of air: 1.2 kg/m3·343 m/s.

The RCL model includes all possible circuits involving a source of damping (a resistor Rac), an acoustic mass or inertance (an inductor Lac), and a source of acoustic compliance (a capacitor Cac). The circuit elements are entered in acoustic units. These can be used as a simple model of, for example, the input impedance of a microphone, a loudspeaker cone, or other electromechanical applications. Other applications include general transmission line/circuit models with applications in materials with exotic acoustic properties. More advanced circuit models may be entered manually in the User defined option or by coupling to an Electrical Circuit model (this requires the AC/DC Module) to a Lumped Port.

Choose an option from the list: Serial coupling RCL, Parallel coupling RCL, Parallel LC in series with R, Parallel RC in series with L, Parallel RL in series with C, Serial RC in parallel with L, Serial LC in parallel with R, or Serial RL in parallel with C.

Notice the matching diagram and Equation section information for each choice. Then enter the following:

This is a set of simple models to address applications involving interactions of acoustics with the human body. The models comprise human skin, the impedance of the entire human ear including or excluding the pinna, the outward radiation impedance caused by the pinna, and the inward impedance experienced at the ear drum comprising the drum and the entire inner ear. For the two models of the human ear (with/without pinna), the pressure at the ear drum is automatically calculated. The variable has the form acpr.imp1.p_ear_drum and is available for postprocessing.

Note that the model for the ear drum impedance (see Ref. 28–30), also known as the model of Hudde and Engel, is defined in the references up to a maximum frequency of 16 kHz. The whole-ear models are based on the geometry of the ear canal and pinna of a specific ear (see Ref. 31 and appendix in Ref. 30), but person-to-person variations are to be expected. The ear canal geometry used here has an ear canal entrance corresponding to a circle of radius 4.25 mm, that is an area of 56.7 mm2. For applications where a specific ear canal geometry can be obtained, better results are expected by explicitly modeling this and applying the eardrum impedance at the end. For more details see the theory sections for the Human skin model and Models related to the human ear.

Choose an option from the list: Human skin, Outward human ear radiation, Human ear drum, Human ear without pinna, or Human ear, full. Then select material properties either From material (the default) or User defined, for the properties of air (the fluid). These are used to define the losses in the fluid. Select as required:

When the From material option is selected, remember to add a material under the Materials node and assign it to the specific boundary. The boundary will not automatically assume the physical properties of the domain.

Choose an option from the list: Flanged pipe, circular (the default), Flanged pipe, rectangular, Unflanged pipe, circular (low ka limit), or Unflanged pipe, circular. Then enter the following as required:

This choice models the acoustic losses of an incident field on a porous layer of user-defined thickness d backed by a sound-hard wall. The angle of incidence can be controlled to be normal to the surface or to use a specific angle or direction. An automatic option assigns an effective angle of incidence useful for room acoustics simulation. Use this boundary condition as an alternative to modeling the porous layer explicitly using the Poroacoustics feature. All material models from Poroacoustics are implemented in this feature.

Note that the Porous Layer condition is not compatible with the Anisotropic Acoustics domain condition. To model a porous layer next to an Anisotropic Acoustics domain, it has to be modeled as a domain using the Poroacoustics feature.

Enter the Thickness of porous layer d (Si unit: m), select the Direction of incident wave, and select a Poroacoustic model. The rest of the settings are the same as for Poroacoustics. For the Direction of incident wave select Normal, Automatic, User defined, or From angle of incidence.

This is a set of models describing the specific characteristic impedance associated with three basic wave types (ratio of local particle velocity to pressure): plane wave, cylindrical wave, and spherical wave. Although mostly of academic interest, these serve as good first-order and wave-type specific boundary-condition models of infinite domains (open boundaries). They can be applied to all cases where the tangential components of the acoustic field at the boundary may be ignored, that is when the angle of incidence is well defined and the wave direction is well known. Use the radiation conditions (Plane Wave Radiation, Spherical Wave Radiation, or Cylindrical Wave Radiation) if a nonreflecting open boundary is modeled.

Select a Wave type: Plane wave (the default), Cylindrical wave, or Spherical wave. Then enter the Wave direction ek for the plane wave (default is normal to the surface); the Radiating field source location r0 and Radiating field source axis rax for the cylindrical wave; or the Radiating field source location r0 for the spherical wave.

With this option the specific impedance of a boundary is defined through the normal incidence absorption coefficient αn (SI unit: 1) of the boundary. Since the absorption coefficient carries no phase information, it is also possible to define the phase of the associated reflection coefficient. If no phase is entered, the impedance will be purely resistive (no reactive component is defined). This is typically an acceptable approximation at higher frequencies and it is also the assumption in ray tracing models. Sometimes surfaces are only specified through an absorption coefficient and in such cases using the Absorption coefficient option can be a first good approximation.

Enter the Normal incidence absorption coefficient αn (SI unit: 1) and the Phase (SI unit: rad).

For the RCL and the Physiological options this section is also visible. The impedance models are defined through an acoustic impedance (the surface area is necessary) and not a specific impedance.

For the Area select Use symmetries or Selected boundaries. For Use symmetries the effective area is computed taking Symmetry boundary conditions into account (if present). An Area multiplication factor Ascale is automatically computed. If necessary select the User defined option and enter a value for Ascale. When Selected boundaries is selected the area is computed only for the boundaries in the selection.