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 in fluids 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 
"RegionSymmetry" None 
"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
- A possible choice for the parameter "RegionSymmetry" is "Axisymmetric".
- "Axisymmetric" region symmetry represents a truncated cylindrical coordinate system where the cylindrical coordinates are reduced by removing the angle variable as follows:
-
dimension reduction equation 1D 
2D 
- If the AcousticPDEComponent depends on parameters
that are specified in the association pars as …,keypi…,pivi,…], the parameters 
are replaced with 
.
Examples
open allclose allBasic 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:
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:
Visualize the sound field in the frequency domain at various frequencies 
:
Scope (21)
Define a time- or frequency-independent acoustic model:
Define a time- or frequency-independent acoustic axisymmetric model:
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:
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 
:
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:
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:
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 
:
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:
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:
Frequency Domain (10)
Define a frequency domain acoustic model with particular sound speed and mass density:
Define a frequency domain acoustic model for a particular material:
Define a frequency domain acoustic model for a particular material:
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:
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 
:
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:
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:
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 
:
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:
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:
Visualize the solution in the frequency domain at various frequencies 
:
Text
Wolfram Research (2020), AcousticPDEComponent, Wolfram Language function, https://reference.wolfram.com/language/ref/AcousticPDEComponent.html (updated 2023).
CMS
Wolfram Language. 2020. "AcousticPDEComponent." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2023. https://reference.wolfram.com/language/ref/AcousticPDEComponent.html.
APA
Wolfram Language. (2020). AcousticPDEComponent. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/AcousticPDEComponent.html