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, Zi is the specific acoustic input 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 acoustic impedance Zi 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
All built-in impedance models only exist in the frequency domain. The only exception is the User defined impedance, which can be applied also in the time domain. In the frequency domain, the impedance can be any complex-valued number and thus models a surface that is both resistive and reactive. In the time domain, only resistive (real-valued impedance) effects can be included.
Enter the value of the Impedance Zi (SI unit: Pa·s/m). The default value is set to the characteristic-specific impedance of air: 1.2 kg/m
3·343 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 Electric Circuit model (this requires the AC/DC Module).
Notice the matching diagram and Equation section information for each choice. Then enter the following:
The whole-ear models are based on the geometry of the ear canal and pinna of a specific ear (see Ref. 28-
30), but person-to-person variations are to be expected. 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.
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 either
From material (the default) or
User defined for the following, 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 a normally incident field on a porous layer of user-defined thickness d backed by a sound-hard wall. 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.
Enter the Thickness of porous layer d (Si unit: m) and select a
Poroacoustic model. The rest of the settings are the same as for
Poroacoustics.
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 rac 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.