# AcousticPDEComponent AcousticPDEComponent[vars,pars]

yields an acoustic PDE term component with variables vars and parameters pars.

# Details    • AcousticPDEComponent returns a sum of differential operators to be used as a part of partial differential equations:
• • AcousticPDEComponent models the propagation of sound in isotropic media in both the time and frequency domain by mechanisms such as diffusion.
• • AcousticPDEComponent models acoustic phenomena with dependent variable pressure in , independent variables in and time variable in or frequency variable in .
• Time-dependent variables vars are vars={p[t,x1,,xn],t,{x1,,xn}}.
• Frequency-dependent variables vars are vars={p[x1,,xn],ω,{x1,,xn}}.
• The time domain acoustics model AcousticPDEComponent is based on a wave equation with time variable , density , sound speed and sound sources and :
• • The frequency domain acoustics model AcousticPDEComponent is based on a Helmholtz equation with angular frequency :
• • The units of the acoustic PDE terms are in .
• The following parameters pars can be given:
•  parameter default symbol "DipoleSource" {0,…} , dipole source in "MassDensity" 1 , density of media in "Material" Automatic "MonopoleSource" 0 , monopole source in "SoundSpeed" 1 , speed of sound in • All parameters may depend on any of , and as well as other dependent variables with the exception of , resulting in a nonlinear eigenvalue problem.
• AcousticPDEComponent allows for sources in the time domain and sources in the frequency domain.
•  Monopole source, Dipole source, • A monopole source models a point source that radiates sound isotropically.
• A dipole source models a two-point source that radiates sound anisotropically.
• The number of independent variables in specifies the length of .
• If no parameters are specified, the default time domain acoustics PDE is
• • If no parameters are specified, the default frequency domain acoustics PDE is
• • If the AcousticPDEComponent depends on parameters that are specified in the association pars as ,keypi,pivi,], the parameters are replaced with .

# Examples

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## Basic Examples(4)

Define a time domain acoustic PDE term:

Define a frequency domain acoustic model:

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

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

Set up the equation with a sound hard boundary at the right end:

Solve the PDE:

Visualize the sound field in the time domain:

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 end:

Solve the PDE:

Visualize the sound field in the frequency domain at various frequencies :

## Scope(20)

Define a time- or frequency-independent acoustic model:

Define a frequency domain acoustic model with particular sounds speed and mass density:

Define a frequency domain acoustic model for a particular material:

Define a frequency domain acoustic model for a particular material:

### Time Domain(7)

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

Set up initial conditions ics of a right-going plane wave :

Set up the equation with an acoustic absorbing boundary at the right end for a plane wave:

Solve the PDE:

Visualize the solution:

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 transient acoustic pressure field with model parameters pars:

Define silent initial conditions ics:

Set up the equation with an acoustic normal velocity boundary with the sound particle velocity v of at the left end:

Solve the PDE on a refined mesh:

Visualize the solution:

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

Define silent initial conditions ics:

Set up the equation with an acoustic pressure boundary and a pressure source of at the left end:

Solve the PDE on a refined mesh:

Visualize the solution:

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

Define silent initial conditions ics:

Set up the equation with an acoustic radiation boundary at the left end, a pressure source of and a radiation angle of :

Solve the PDE:

Visualize the solution:

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 sound hard boundary at the right end:

Solve the PDE:

Visualize the solution:

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

Define initial conditions of a right-going plane wave :

Set up the equation with an acoustic sound soft boundary at the right end:

Solve the PDE:

Visualize the solution:

### Frequency Domain(7)

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 end and an acoustic absorbing boundary at the right end:

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 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 frequency domain acoustic pressure field with model parameters pars:

Set up the equation with an acoustic normal velocity boundary at the left, the sound particle velocity of and an acoustic absorbing boundary at the right:

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 frequency domain acoustic pressure field with model parameters pars:

Set up the equation with an acoustic pressure boundary at the left, a pressure source of and an acoustic absorbing boundary at the right:

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 frequency domain acoustic pressure field with model parameters pars:

Set up the equation with an acoustic radiation boundary at the left end, a pressure source of and a radiation angle 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 frequency domain acoustic pressure field with model parameters pars:

Set up the equation with an acoustic radiation boundary at the left, a pressure source of and an acoustic sound hard boundary at the right:

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 frequency domain acoustic pressure field with model parameters pars:

Set up the equation with a radiation boundary at the left end and an acoustic absorbing boundary at the right end:

Solve the PDE:

Visualize the solution in the frequency domain at various frequencies :

Convert the solution to the time domain:

### Units(2)

Set up an acoustic time domain equation for aluminum:

Set up an acoustic frequency domain model for aluminum by specifying material parameters: