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:
  • parameterdefaultsymbol
    "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:

Wolfram Research (2020), AcousticPDEComponent, Wolfram Language function, https://reference.wolfram.com/language/ref/AcousticPDEComponent.html.

Text

Wolfram Research (2020), AcousticPDEComponent, Wolfram Language function, https://reference.wolfram.com/language/ref/AcousticPDEComponent.html.

BibTeX

@misc{reference.wolfram_2021_acousticpdecomponent, author="Wolfram Research", title="{AcousticPDEComponent}", year="2020", howpublished="\url{https://reference.wolfram.com/language/ref/AcousticPDEComponent.html}", note=[Accessed: 27-November-2021 ]}

BibLaTeX

@online{reference.wolfram_2021_acousticpdecomponent, organization={Wolfram Research}, title={AcousticPDEComponent}, year={2020}, url={https://reference.wolfram.com/language/ref/AcousticPDEComponent.html}, note=[Accessed: 27-November-2021 ]}

CMS

Wolfram Language. 2020. "AcousticPDEComponent." Wolfram Language & System Documentation Center. Wolfram Research. 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