Acoustics Module
Acoustics Module
Software for Acoustics and Vibration Analysis
Bringing Acoustics and Vibration Analysis to a New Level
The Acoustics Module is designed specifically for those who work with devices that produce, measure, and utilize acoustic waves. Application areas include speakers, microphones, hearing aids, and sonar devices, to name a few. Noise control can be addressed in muffler design, sound barriers, buildings, and room acoustics applications.
Gain Insight Into New and Existing Products and Designs
Straightforward user interfaces provide tools for modeling acoustic pressure wave propagation in air, water, and other fluids. Dedicated modeling tools for thermoviscous acoustics enable highly accurate simulation of miniaturized speakers and microphones in handheld devices. You can also model vibrations and elastic waves in solids, piezoelectric materials, and poroelastic structures.
Multiphysics interfaces for acousticsolid, acousticshell, and piezoacoustics couplings bring your acoustic simulations to a new level of predictive power. Aeroacoustic problems can be modeled using one of several linearized equation approaches. Room and outdoor acoustics problems can be modeled using ray tracing or acoustic diffusion methods.
By using realistic simulations in 1D, 2D, 2D axisymmetry, or 3D, you can optimize existing products and design new products more quickly. Simulations also help designers, researchers, and engineers to gain insight into problems that are difficult to handle experimentally. By testing a design before manufacturing it, companies save both time and money.
Additional Images:
 The sound pressure level distribution in a muffler system.
 This simulation of a concert hall uses ray acoustics to determine the sound pressure around the stage and seating area.
 The tonpilz (sound mushroom) piezo transducer is a transducer for relatively lowfrequency, highpower sound emission. The transducer consists of piezoceramic rings stacked between massive ends, and prestressed by a central bolt. The tail and head mass lower the resonance frequency of the device.
 Poroelastic waves and acoustics in a conceptual particulatefilter system. Diesel particulate filters (DPFs), are designed to remove/filter soot (diesel particles) from the exhaust of diesel engine vehicles. Although the main function of a particulate filter is to filter the exhaust flow, it also has acoustic damping properties that relate to the muffler system.

This is a model of the Brüel and Kjær 4134 condenser microphone. The geometry and material parameters are those of the actual microphone. The modeled sensitivity level is compared to measurements performed on an actual microphone and shows good agreement. The membrane deformation, pressure, velocity, and electric field are also determined. Model provided courtesy Brüel & Kjær Sound & Vibration Measurement, Nærum, Denmark.
 The visualization shows isosurfaces of the acoustic pressure in a car interior. LiveLink™ for Inventor^{®} allows users to access COMSOL functionality directly from within the Inventor^{®} user interface including that of the Acoustics Module.
For Modeling a Variety of Different Acoustics Applications
The Acoustics Module consists of a set of physics interfaces – user interfaces with associated modeling and simulation tools – that enable you to simulate the propagation of sound in fluids and solids. Within the Acoustics Module, these are organized into pressure acoustics, acousticstructure interaction, aeroacoustics, thermoviscous acoustics, ultrasound, and geometrical acoustics.
Acoustic simulations performed using the physics interfaces for pressure acoustics can easily model classic problems such as scattering, diffraction, emission, radiation, and the transmission of sound. These problems are relevant to muffler design; loudspeaker construction; sound insulation for absorbers and diffusers; the evaluation of directional acoustic patterns, like directivity; noise radiation problems; and much more.
The physics interfaces for acousticstructure interaction model problems involving the interaction between structural elastic waves and fluidborne sound. For example, acousticstructure interaction is considered in detailed muffler design, ultrasound piezoactuators, sonar technology, and noise and vibration analyses of machinery. Using COMSOL Multiphysics, this capability enables you to analyze and design electroacoustic transducers, including loudspeakers, sensors, microphones, and receivers.
The Aeroacoustics physics interfaces are used to model the oneway interaction between an external flow and an acoustic field, (fluidborne noise). Applications range from jetengine noise analysis to wind sensor simulation.
The physics interfaces for geometrical acoustics include Ray tracing and the Acoustic diffusion equation interfaces. Both interfaces are applicable for modeling acoustics in rooms and buildings. Ray tracing is also used, for example, in ocean acoustics and atmosphere acoustics.
Thermoviscous acoustic applications are accurately modeled using the provided, appropriate physics interfaces. These are applications that include small geometrical dimensions where the thermal and viscous fluid properties need to be considered, for example, cell phones, hearing aids, MEMS applications, and transducer designs.
Multiphysics Couplings
Completely integrated in the COMSOL Multiphysics^{®} environment, the Acoustics Module can be combined with other modules for a wider range of multiphysics simulations. Such is the case for the multiphysics interfaces for acousticshell interaction and thermoviscous acousticshell interaction, which are available when combining the Acoustics Module with the Structural Mechanics Module. Similarly, physics interfaces for pipe acoustics are available when combining the Acoustics Module with the Pipe Flow Module.
Multiphysics couplings and predefined multiphysics interfaces are set up in COMSOL Multiphysics by introducing a Multiphysics node. For example, coupling the physics describing pressure acoustics in a fluid domain to the physics describing structural mechanics in a surrounding solid is achieved in COMSOL Multiphysics by adding an Acoustics interface and a Solid Mechanics interface separately and then coupling them at the boundary using the relevant coupling under the multiphysics node. This functionality makes it possible to decouple or oneway couple the two contributing physics, as well as giving full control over all functionalities in the Acoustics and Solid Mechanics interfaces.
Among the many multiphysics couplings available are the AcousticStructure Boundary, the AeroacousticStructure Boundary, and the Thermoviscous AcousticStructure Boundary multiphysics interfaces. These all couple a fluid domain to a structure that includes a solid, an external or internal shell, or a membrane. Also available are the AcousticThermoviscous Acoustic Boundary, AcousticPorous Boundary, and PorousStructure Boundary multiphysics interfaces, while the Piezoelectric Effect multiphysics interface connects a Solid Mechanics interface and an Electrostatics interface for modeling piezoelectric materials. All multiphysics models are fully coupled by default, while oneway coupling and dissociating the couplings can be achieved by manipulating the Multiphysics node.
Consistent Workflow
The Acoustics Module adheres to the same workflow as any other addon module in the COMSOL^{®} Product Suite. All modeling steps are accessed from the COMSOL Desktop^{®} and include defining the geometry, selecting materials, selecting a suitable physics interface, defining boundary and initial conditions, automatically creating the finite element mesh, solving, and visualizing the results. Acoustic simulations can be coupled with any other COMSOL Multiphysics^{®} addon product in just about any way imaginable by a suite of preset multiphysics couplings, such as with the Structural Mechanics Module for acousticshell interaction, or by userdefined couplings. The Optimization Module can be combined with the Acoustics Module for optimizing geometric dimensions, acoustic transmission, and more.
Connecting the Acoustics Module with CAD, MATLAB^{®}, and Excel^{®}
For repetitive modeling tasks, LiveLink™ for MATLAB^{®} makes it possible to drive COMSOL^{®} simulations with MATLAB^{®} scripts or functions. Any operation available in COMSOL Desktop^{®} can alternatively be accessed through MATLAB^{®} commands. You can also include COMSOL^{®} commands in the MATLAB^{®} environment with your existing MATLAB^{®} code.
For acoustic simulations driven from spreadsheets, LiveLink™ for Excel^{®} offers a convenient alternative to modeling from COMSOL Desktop^{®} with synchronization of spreadsheet data with parameters defined in the COMSOL^{®} environment. The CAD Import Module and LiveLink™ products for leading CAD systems makes it easy to perform acoustic simulations using CAD models. The LiveLink™ products make it possible to keep the parametric CAD model intact in its native environment but still control the geometric dimensions from within COMSOL Multiphysics^{®}. Linking your acoustics models to CAD products allows you to simultaneously perform parametric sweeps over several model parameters.
Flexible and Robust Acoustics Modeling
The equations within the Acoustics Module are solved using the finite element method with higherorder element discretization in combination with stateoftheart solvers. The different formulations cover both frequency and timedomain simulations. Your results are presented in the graphics window through preset plots of acoustic and displacement fields, sound pressure levels, stresses and strains, or as expressions of physical quantities that you can define freely, as well as derived tabulated quantities.
Simulations Including Acoustic Losses
The Acoustics Module is shipped with an extensive Model Library with many examples of applications ranging from modeling sound insulation lining, loudspeakers, microphones, and mufflers. Many of these examples show how to simulate acoustic losses. The loss models of the Acoustics Module range from empirical equivalentfluid models for fibrous materials, solving Biot's theory in the Poroelastic Waves interface, to a fullyfledged thermal and viscous loss model using the Thermoviscous Acoustics interface.
Easytouse Physics Interfaces for Acoustics Analysis
Pressure Acoustics
The Pressure Acoustics interfaces describe and solve sound fields through a scalar acoustic pressure field, which represents acoustic variations (or excess pressure) with respect to the ambient stationary pressure. They enable solving either in the frequency domain, where the Helmholtz equation is solved, or as a transient system, where the classical scalar wave equation is solved. A special physics interface for boundary mode acoustics is used to study propagating modes in waveguides and ducts, and is based on the fact that only a finite set of shapes, or modes, can propagate over longer distances.
A large variety of boundary conditions are available and include hard walls and impedance conditions, radiation, symmetry, and periodic conditions for modeling open boundaries as well as conditions for applying sources. The interfaces also contain several equivalentfluid models, which mimic the behavior of sound propagation in more complex media. Several poroacoustics fluid models prescribe losses in porous or fibrous materials. Narrow region acoustics models add the thermoviscous losses associated with hard boundaries in narrow regions. Attenuation can be added as a userdefined relation, or it can be calculated for viscous and thermally conducting fluids. Perfectly matched layers (PMLs) are also available to truncate the computational domain by absorbing outgoing acoustic waves, thereby mimicking an infinitely extended domain. They exist on both the frequency and time domain.
When your calculations have been performed, a farfield feature can be used to determine the pressure and phase information at any distance outside the computational domain. Dedicated results and analysis capabilities are available for visualizing the farfield with polar plots in 2D and 3D.
AcousticStructure Interaction
Coupling fluid and structural domains is achieved by using the predefined multiphysics interfaces of the Acoustics Module, which automatically set up the relevant physics and multiphysics couplings. From one side of the fluidsolid boundary, the AcousticStructure Boundary interfaces handles the fluid pressure that acts on the solid domain and, from the other, the structural accelerated displacement that acts on the fluid domain. Multiphysics couplings encompass applications involving acousticsolid, acousticshell, and acousticpiezoelectric interactions – all within the frequency and time domains, and in 3D, 2D, and 2D axisymmetric geometric models. The couplings involving structural shells are available when combining the Acoustics Module with the Structural Mechanics Module, where you are also able to access more advanced structural modeling capabilities.
Elastic waves are an important application area for acousticians. With the Acoustics module you can use the Solid Mechanics interface to get a full structuraldynamics formulation that includes all the effects of shear waves and pressure waves in solids.
The AcousticPiezoelectric Interaction multiphysics interfaces not only simulate the acousticstructure interaction with great accuracy, but also supports solving and modeling the electric field in the piezoelectric material. When combined with the AC/DC Module or the MEMS Module, you can also combine piezoelectric simulations with SPICE circuits. This capability is excellent when, for example, using lumped models to describe some of the electrical behavior of a transducer while using the full finite element description for the other physics.
The Pipe Acoustics interfaces (available together with the Pipe Flow Module) are used for 1D modeling of the propagation of sound waves in flexible pipe systems. The equations are formulated in a general way to include the effects of the pipe wall compliance with the possibility of a stationary background flow.
Using Biot’s theory, the Poroelastic Waves interface accurately models the propagation of sound in a porous material, including the twoway coupling between deformation of the solid matrix and the pressure waves in the saturating fluid through a dedicated multiphysics boundary condition that enables easy coupling of the porous domain and a fluid domain.
Geometrical Acoustics
The Geometrical Acoustics branch includes the Ray Acoustics and the Acoustic Diffusion Equation physics interfaces. The physics in both interfaces are valid in the highfrequency limit where the acoustic wavelength is smaller than the characteristic geometric features. This is at frequencies above the Schroeder frequency for rooms. Both interfaces are suited for modeling acoustics in rooms and buildings like concert halls. The Acoustic Diffusion Equation is restricted to indoor applications whereas the Ray Acoustics interface can be used, for example, in ocean acoustics and atmosphere acoustics. The acoustic properties at boundaries are included through different models for the absorption.
The Ray Acoustics physics interface is used to compute the trajectories, phase, and intensity of acoustic rays. Ray acoustics is valid in the highfrequency limit where the acoustic wavelength is smaller than the characteristic geometric features. The interface can be used to model acoustics in rooms, concert halls, schools, office buildings, and many outdoor environments. The properties of the media in which the rays propagate can change continuously within domains (graded media) or discontinuously at boundaries. At exterior boundaries, it is possible to assign a variety of wall conditions, including combinations of specular and diffuse reflection. Impedance and absorption can depend on the frequency, intensity, and direction of incident rays. Transmission and reflection are also modeled at material discontinuities. A background velocity may also be assigned to any medium.
The Acoustic Diffusion Equation interface solves a diffusion equation for the acoustic energy density. It is applicable for highfrequency acoustics where the acoustic fields are diffuse. The diffusion properties are dependent on both the room geometry and absorption properties of walls, room fittings (uses average volumetric absorption based on average crosssection and attenuation), and volumetric attenuation (viscous and thermal in large volumes only). The interface is well suited for quick assessment of sound pressure level distribution inside buildings and other large structures.
The Acoustic Diffusion Equation interface can be used to determine the reverberation times at different locations. This can be done either by performing a transient analysis and looking at the energy decay curve, or by performing an eigenvalue analysis. Inputs for all sources, absorption parameters, and transmission losses can be determined using one of the bands, provided in the module. Using these input types and a parametric sweep over the studied band, the user can easily plot and analyze the model results to express results in these bands.
Aeroacoustics
Ideally, computational aeroacoustic (CAA) simulations would involve solving the fully compressible NavierStokes equations in the time domain. The acoustic pressure waves would then form a subset of the fluid solution. This approach is often impractical for realworld applications due to the required computational accuracy necessary, the computational time, and memory resources. For solving many practical engineering problems, a decoupled twostep approach is used instead: first solve for the background mean fluid flow, then for the acoustic perturbations of the flow. This very important oneway interaction is also known as a fluidborne noise/sound phenomenon.
The primary tools in the Acoustics Module for fluidborne sound is the Linearized Euler and the Linearized NavierStokes physics interfaces, while the Linearized Potential Flow interfaces provides a more simplified approach.
The Linearized NavierStokes interfaces are used to compute the acoustic variations in pressure, velocity, and temperature in the presence of any stationary isothermal or nonisothermal background meanflow. The interfaces are used for aeroacoustics simulations that can be described by the linearized NavierStokes equations. The equations include viscous losses and thermal conduction as well as the heat generated by viscous dissipation. The coupling between the acoustic field and the background flow does not include any predefined flowinduced noise. Application examples for aeroacoustics with the linearized NavierStokes equations include analyzing the attenuation properties of mufflers in the presence of turbulent flow or the performance of liners and perforates with grazing or normal flows. Coupling the Linearized NavierStokes, Frequency Domain interface to structures using the AeroacousticStructure Boundary multiphysics coupling enables a detailed vibration analysis of structures in the presence of flow (for example, modeling Coriolis flow meters).
The Linearized Euler interfaces are used to compute the acoustic variations to pressure, velocity, and density for a given background meanflow. They solve for the linearized Euler equations, including the energy equation, with the assumptions that the background flow is an ideal gas (or is wellapproximated by an ideal gas) and that there are no thermal or viscous losses. The Linearized Euler physics interfaces are available for time domain, frequency domain, and eigenfrequency analyses. Application examples for aeroacoustics with the linearized Euler equations include analyzing the propagation of noise from jet engines or the interaction of gusts and waves with blade profiles. These are situations where a gas background flow influences the propagation of acoustic waves in the fluid and losses can be disregarded.
For simplified oneway interactions, the Linearized Potential Flow interfaces are available in both the frequency and transient domains, and utilize formulations based on a fluidpotential. Moreover, the Compressible Potential Flow interface is used to model the background mean flow of an inviscid, compressible fluid that has no vorticity as it is irrotational by nature. Finally, the Linearized Potential Flow, Boundary Mode interface is used to study boundary mode acoustic problems in a background flow field, typically used to specify sources at inlets.
Thermoviscous Acoustics
The Acoustics Module provides stateoftheart modeling capabilities for thermoviscous acoustics (also known as viscothermal acoustics), which is critical for accurate simulation of acoustics in geometries with small dimensions. Close to walls, viscosity and thermal conduction become important as a viscous and thermal boundary layer are created, resulting in significant losses. This makes it necessary to include thermal conduction effects and viscous losses explicitly in the governing equations.
The physics interfaces for thermoviscous acoustics are used to solve for the full set of linearized compressible flow equations with zero background flow, that is, the linearized NavierStokes, continuity, and energy equations all together. Because a detailed description is needed to model thermoviscous acoustics, all the physics interfaces simultaneously solve for the acoustic pressure, the particle velocity vector, and the acoustic temperature variation.
The Thermoviscous Acoustics interface exists in both the frequency and time domain. Both mechanical and thermal boundary conditions are available. Coupling the thermoviscous acoustic domain to a pressure acoustic domain is also straightforward with a predefined multiphysics boundary condition. A Thermoviscous AcousticStructure Boundary multiphysics coupling is available, and makes it easy to solve for coupled vibroacoustics. You can, for example, use it to model small electroacoustic transducers or damping in MEMS devices. It can also be used to analyze the interaction between shells and acoustics in small dimensions, for example, the damped vibrations of shells in hearing aids to prevent feedback problems.
The Thermoviscous Acoustics, Boundary Mode interface is used to compute and identify propagating and nonpropagating modes in waveguides and ducts. The interface performs a boundary mode analysis on a boundary, inlet, or cross section of a waveguide or duct of small dimensions, including the thermal and viscous loss effects that are important in the acoustic boundary layer near walls. The interface can be used when setting up sources in systems with small ducts, like hearing aids or mobile devices, for example.
Ultrasound
The Ultrasound interfaces are used to compute the transient propagation of acoustic waves over large distances, relative to the wavelengths. Acoustic disturbances with frequencies that are not audible for humans are classified as ultrasound. This implies that ultrasonic waves have a short wavelength. The interfaces under the Ultrasound branch are, however, not restricted to highfrequency propagation, but can, in general, be applied to any acoustically large problem.
The Convected Wave Equation, Time Explicit interface is used to solve large transient linear acoustic problems containing many wavelengths in a stationary background flow. It is suited for timedependent simulations with arbitrary timedependent sources and fields. In general, the interface is suited for modeling the propagation of acoustic signals over large distances relative to the wavelength, for example, linear ultrasound problems. The interface includes absorbing layers that are used to set up effective nonreflecting like boundary conditions. The interface is based on the discontinuous Galerkin method and uses a timeexplicit solver. The method is very memory lean. Application areas include ultrasound flow meters and other ultrasound sensors where time of flight is an important parameter. The applications are not restricted to ultrasound, but also include, for example, transient propagation of audio pulses in room acoustics or car cabins.
Helmholtz Resonator with Flow: Interaction of Flow and Acoustics
Helmholtz resonators are used in exhaust systems, as they can attenuate a specific narrow frequency band. The presence of a flow in the system alters the acoustic properties of the resonator and the transmission loss of the subsystem. In this tutorial model, a Helmholtz resonator is located as a side branch to a main duct. The transmission loss ...
Absorptive Muffler
The sound level from a car depends to a great extent of the quality of the muffler. Over the years, researchers in the car industry have struggled to produce mufflers that are efficient from both an acoustic and an environmental perspective. This model describes the pressure wave propagation in a muffler for an internal combustion engine. The ...
Flow Duct
The modeling of aircraftengine noise is a central problem in the field of computational aeroacoustics. The acoustic field in a model of an axially symmetric aeroengine duct, generated by a noise source at the boundary, is computed and visualized. Results are presented for situations with as well as without a compressible irrotational ...
Ultrasonic Flow Meter with Piezoelectric Transducers: Coupling between FEM and DG
Ultrasonic flow meters determine the velocity of a fluid flowing through a pipe by sending an ultrasonic signal across the flow at a skew angle. When there is no flow, the transmitting time between the transmitter and the receiver is the same for the signals sent in the upstream and downstream directions. Otherwise, the wave traveling downstream ...
Sedan Interior Acoustics
This is a model of the acoustics inside a sedan, that is inside a typical hardtop family car. The model sets up sources at loudspeaker locations as well as impedance conditions to model soft absorbing surfaces for the seats, carpet, and roof lining. The model results in plots of the pressure, sound pressure level, and intensity inside the car. ...
Loudspeaker Driver
This example shows you how to model a loudspeaker of the dynamic cone driver type, common for low and medium frequencies. The model analysis includes the total electric impedance and the onaxis sound pressure level at a nominal driving voltage, as functions of the frequency. The spatial characteristics of the speaker are depicted in a ...
Transfer Impedance of a Perforate
Perforates are plates with a distribution of small perforations or holes. They are used in muffler systems, sound absorbing panels, and in many other places as liners, where it is important to control attenuation precisely. As the perforations become smaller and smaller, viscous and thermal losses become more important. The attenuation behavior, ...
Focused Ultrasound Induced Heating in Tissue Phantom
This model example shows how to model tissue heating induced by focused ultrasound. First, the stationary acoustic field in the water and the tissue are modeled to obtain the acoustic intensity distribution in the tissue. The absorbed acoustic energy is then calculated and used as the heat source for a Bioheat Transfer physics in the tissue ...
Surface Acoustic Wave Gas Sensor
A surface acoustic wave (SAW) is an acoustic wave propagating along the surface of a solid material. Its amplitude decays rapidly, often exponentially, through the depth of the material. SAWs are utilized in many kinds of electronic components, including filters, oscillators, and sensors. SAW devices typically apply electrodes to a piezoelectric ...
Ultrasound Flow Meter with Generic TimeofFlight Configuration
Knowing the velocity of a moving fluid is important in all cases where the fluid is used to transport material or energy. In the timeofflight or transittime method for determining flow velocity, an ultrasonic signal is transmitted across the main flow in a pipe to noninvasively determine its velocity. By transmitting the signal at an angle ...