Set up a time domain acoustic impedance boundary:

Set up a frequency domain acoustic impedance boundary:

Set up a time-independent acoustic impedance boundary:

Define model variables vars for a transient acoustic pressure field with model parameters pars:

Define initial conditions ics of a right-going plane wave :

Set up the equation with an acoustic impedance boundary at the right and an impedance of :

Solve the PDE:

Visualize the solution:

Define model variables vars for a frequency domain acoustic pressure field with model parameters pars:

Set up the equation with a radiation boundary at the left, an acoustic impedance boundary at the right and an impedance of :

Solve the PDE:

Visualize the solution in the frequency domain at various frequencies :

Convert the solution to the time domain:

Define model variables vars for a transient acoustic pressure field with model parameters pars and a specific boundary condition parameter:

Define model variables vars for a transient acoustic pressure field with model parameters pars and multiple specific parameters boundary conditions:

The following acoustic model describes an open pipe, wherein a vibrating piston is placed inside one end of the pipe while the other end of the pipe opens into an infinite domain. In this case, an impedance boundary condition is placed on one end to model the infinite domain. The pipe that will be modeled is a flanged circular pipe, as shown in the following figure below:

Since the geometry of the pipe and the boundary conditions are rotationally symmetric about the axis, an axisymmetric model can be used. The governing equation for describing the sound wave propagation is the axisymmetric Helmholtz equation.

Set up the variables and parameters:

The axisymmetric geometry can be approximated by a 2D rectangle, which represents a cross-section of the pipe in the plane:

Set up the rectangle region with as the radius of the tube and as the length of the tube:

In the model, there are two boundary conditions. One is a NeumannValue that expresses the acceleration of the piston with :

The second boundary condition is an AcousticImpedanceValue with impedance . The impedance is given by the following approximation, where is the wavenumber:

Set up the equation:

Solve the PDE with with a MaxCellMeasure defined by and with a resolution of 12 to get an accurate result:

Visualize the pressure distribution in the full 3D region:

The default value for "SpecificAcousticImpedance" is Infinity:

Set a different value for the "SpecificAcousticImpedance":