AcousticRadiationValue
✖
AcousticRadiationValue
represents a time or frequency radiation boundary condition for PDEs with predicate pred indicating where it applies, with model variables vars and global parameters pars.
represents a time or frequency domain boundary condition with local parameters specified in pars[lkey].
Details
- AcousticRadiationValue specifies a boundary condition for AcousticPDEComponent and is used as part of the modeling equation:
- AcousticRadiationValue is typically used to model sound sources and sinks on the boundary.
- AcousticRadiationValue models a time or frequency domain boundary source or sink with dependent variable pressure
in 
, independent variables 
in 
and time variable 
in 
or frequency variable 
in 
. - Time-dependent model variables vars are vars={p[t,x1,…,xn],t,{x1,…,xn}}.
- Frequency-dependent model 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 time domain radiation value AcousticRadiationValue with boundary pressure source
, boundary unit normal vector 
and unit wave direction vector 
models: - The frequency domain radiation value AcousticRadiationValue models:
- The dipole source
will only be valid within the domain and thus can be excluded from the boundary conditions. - Model parameters pars are specified as for AcousticPDEComponent.
- The following model parameters pars can be given:
-
parameter default symbol "BoundaryUnitNormal" Automatic 
"MassDensity" 1 
, density of media in 
"Material" Automatic 
"SoundSpeed" 1 
, speed of sound in 
"SoundDirectionVector" 
, sound direction vector"SoundIncidentPressure" 0 
, sound pressure in 
- The relation between the outward-pointing boundary unit normal vector
and the incident sound wave direction vector 
is illustrated in the following: - AcousticRadiationValue combines an AcousticPressureCondition and an AcousticAbsorbingValue.
- AcousticRadiationValue evaluates to a generalized NeumannValue.
- The boundary predicate pred can be specified as in NeumannValue.
- An absorbing boundary can be used with:
-
analysis type applicable Time Domain Yes Frequency Domain Yes Eigenfrequency No - If the AcousticRadiationValue depends on parameters
that are specified in the association pars as …,keypi…,pivi,…], the parameters 
are replaced with 
.
Examples
open allclose allBasic Examples (4)Summary of the most common use cases
Set up a time domain acoustic radiation boundary:
https://wolfram.com/xid/0mfdtx00jbphniksai-vw7olo
Set up a frequency domain acoustic radiation boundary:
https://wolfram.com/xid/0mfdtx00jbphniksai-u1kv4k
Define model variables vars for a frequency domain acoustic pressure field with model parameters pars:
https://wolfram.com/xid/0mfdtx00jbphniksai-njshna
Define silent initial conditions ics:
https://wolfram.com/xid/0mfdtx00jbphniksai-2uykky
Set up the equation with an acoustic radiation boundary at the left end, a pressure source 
of 
and a radiation angle 
of 
:
https://wolfram.com/xid/0mfdtx00jbphniksai-ybech5
https://wolfram.com/xid/0mfdtx00jbphniksai-hpjmye
https://wolfram.com/xid/0mfdtx00jbphniksai-hb4etn
Define model variables vars for a frequency domain acoustic pressure field with model parameters pars:
https://wolfram.com/xid/0mfdtx00jbphniksai-exrmgh
Set up the equation with an acoustic radiation boundary at the left end, a pressure source 
of 
and a radiation angle 
of 
:
https://wolfram.com/xid/0mfdtx00jbphniksai-gkaaae
https://wolfram.com/xid/0mfdtx00jbphniksai-xht1ym
Visualize the sound field in the frequency domain at various frequencies 
:
https://wolfram.com/xid/0mfdtx00jbphniksai-6luhf0
Convert the solution to the time domain:
https://wolfram.com/xid/0mfdtx00jbphniksai-t1egga
Scope (2)Survey of the scope of standard use cases
Define model variables vars for a transient acoustic pressure field with model parameters pars and a specific boundary condition parameter:
https://wolfram.com/xid/0mfdtx00jbphniksai-glqeii
Define model variables vars for a transient acoustic pressure field with model parameters pars and multiple specific parameters boundary conditions:
https://wolfram.com/xid/0mfdtx00jbphniksai-uwpzeb
https://wolfram.com/xid/0mfdtx00jbphniksai-hwq3hg
https://wolfram.com/xid/0mfdtx00jbphniksai-zk0k6a
Wolfram Research (2020), AcousticRadiationValue, Wolfram Language function, https://reference.wolfram.com/language/ref/AcousticRadiationValue.html.Text
Wolfram Research (2020), AcousticRadiationValue, Wolfram Language function, https://reference.wolfram.com/language/ref/AcousticRadiationValue.html.
Wolfram Research (2020), AcousticRadiationValue, Wolfram Language function, https://reference.wolfram.com/language/ref/AcousticRadiationValue.html.CMS
Wolfram Language. 2020. "AcousticRadiationValue." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/AcousticRadiationValue.html.
Wolfram Language. 2020. "AcousticRadiationValue." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/AcousticRadiationValue.html.APA
Wolfram Language. (2020). AcousticRadiationValue. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/AcousticRadiationValue.html
Wolfram Language. (2020). AcousticRadiationValue. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/AcousticRadiationValue.htmlBibTeX
@misc{reference.wolfram_2025_acousticradiationvalue, author="Wolfram Research", title="{AcousticRadiationValue}", year="2020", howpublished="\url{https://reference.wolfram.com/language/ref/AcousticRadiationValue.html}", note=[Accessed: 08-June-2025
]}BibLaTeX
@online{reference.wolfram_2025_acousticradiationvalue, organization={Wolfram Research}, title={AcousticRadiationValue}, year={2020}, url={https://reference.wolfram.com/language/ref/AcousticRadiationValue.html}, note=[Accessed: 08-June-2025
]}