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AcousticSoundSoftCondition[pred,vars,pars]

represents a time or frequency domain sound soft boundary condition for PDEs with predicate pred indicating where it applies, with model variables vars and global parameters pars.

AcousticSoundSoftCondition[pred,vars,pars,lkey]

represents a time or frequency domain boundary condition with local parameters specified in pars[lkey].

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AcousticSoundSoftCondition

AcousticSoundSoftCondition[pred,vars,pars]

represents a time or frequency domain sound soft boundary condition for PDEs with predicate pred indicating where it applies, with model variables vars and global parameters pars.

AcousticSoundSoftCondition[pred,vars,pars,lkey]

represents a time or frequency domain boundary condition with local parameters specified in pars[lkey].

Details

Examples

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Basic Examples  (3)

Set up an acoustic sound soft boundary:

Wolfram Language code: AcousticSoundSoftCondition[x ≥ 0, {p[t, x, y], t, {x, y}}, <||>]

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

Wolfram Language code: vars = {p[t, x], t, {x}}; pars = <|"SoundSpeed" -> 343, "MassDensity" -> 1.2|>;

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

Wolfram Language code: p0 = D[0.125 Erf[(x - 0.5) / 0.15], x]; ics = {p[0, x] == p0, Derivative[1, 0][p][0, x] == -343 * D[p0, x]};

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

Wolfram Language code: eqn = {AcousticPDEComponent[vars, pars] == 0, AcousticSoundSoftCondition[x == 1, vars, pars]};

Solve the PDE:

Wolfram Language code: pfun = NDSolveValue[{eqn, ics}, p, {t, 0, 0.003}, x∈Line[{{0}, {1}}]];

Visualize the solution:

Wolfram Language code: Manipulate[Plot[pfun[t, x], {x, 0, 1}, ...], {{t, 0.0022}, 0, 0.003, 10 ^ -4}, Rule[...]]

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

Wolfram Language code: vars = {p[x], ω, {x}}; pars = <|"SoundSpeed" -> 343, "MassDensity" -> 1.2|>;

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

Wolfram Language code: eqn = {AcousticPDEComponent[vars, pars] == AcousticRadiationValue[x == 0, vars, pars, <|"SoundIncidentPressure" -> 1|>], AcousticSoundSoftCondition[x == 1, vars, pars]};

Solve the PDE:

Wolfram Language code: pfun = ParametricNDSolveValue[eqn, p, x∈Line[{{0}, {1}}], {ω}];

Visualize the solution in the frequency domain at various frequencies :

Wolfram Language code: Plot[Table[Legended[Abs[pfun[ω][x]], ω], {ω, {1000π, 1500π, 2000π}}]//Evaluate, {x, 0, 1}, ...]

Convert the solution to the time domain:

Wolfram Language code: Plot[Table[Legended[Re[pfun[ω][x] * Exp[I ω t]], ω], {t, {0.01}}, {ω, {1000π, 1500π, 2000π}}]//Evaluate, {x, 0, 1}, ...]

Scope  (2)

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

Wolfram Language code: vars = {p[t, x, y], t, {x, y}}; pars = <|"SoundSpeed" -> 343, "MassDensity" -> 12 / 10, "BoundaryCondition1" -> <||>|>; AcousticSoundSoftCondition[x == 1, vars, pars, "BoundaryCondition1"]

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

Wolfram Language code: vars = {p[t, x, y], t, {x, y}}; pars = <|"SoundSpeed" -> 343, "MassDensity" -> 12 / 10, "BoundaryCondition1" -> <||>, "BoundaryCondition2" -> <||>|>;
Wolfram Language code: AcousticSoundSoftCondition[x == 0, vars, pars, "BoundaryCondition1"]
Wolfram Language code: AcousticSoundSoftCondition[x == 1, vars, pars, "BoundaryCondition2"]
Wolfram Research (2020), AcousticSoundSoftCondition, Wolfram Language function, https://reference.wolfram.com/language/ref/AcousticSoundSoftCondition.html.

Text

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

CMS

Wolfram Language. 2020. "AcousticSoundSoftCondition." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/AcousticSoundSoftCondition.html.

APA

Wolfram Language. (2020). AcousticSoundSoftCondition. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/AcousticSoundSoftCondition.html

BibTeX

@misc{reference.wolfram_2026_acousticsoundsoftcondition, author="Wolfram Research", title="{AcousticSoundSoftCondition}", year="2020", howpublished="\url{https://reference.wolfram.com/language/ref/AcousticSoundSoftCondition.html}", note=[Accessed: 12-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_acousticsoundsoftcondition, organization={Wolfram Research}, title={AcousticSoundSoftCondition}, year={2020}, url={https://reference.wolfram.com/language/ref/AcousticSoundSoftCondition.html}, note=[Accessed: 12-June-2026]}