![Page 1: © 2013 COMSOL. All rights reserved. Living room acoustics](https://reader035.vdocuments.net/reader035/viewer/2022062307/55199ba055034643068b49da/html5/thumbnails/1.jpg)
© 2013 COMSOL. All rights reserved.
Living room acoustics
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Background and Motivation
• This is a model that solves for the Eigenfrequencies and for the acoustic field inside a living room where the sound sources are placed at the loudspeaker location.
• The model enables the user to get the Eigenfrequencies around 90 Hz and the response at any point in the living room up to 500 Hz.
• This is useful when optimizing for loudspeaker locations inside the living room.
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Geometry
• The geometry corresponds to a living room with different furniture:
Loudspeaker boxes
Carpet
Shelf
TV Table
TableTV
Couch
Aluminum legs
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Absorbing and damping boundaries
• The living room has many surfaces that are not sound-hard but rather act as absorbers. The couch is for example made of a porous material like, for example, foam covered with tissue or leather.
• These surfaces can be modeled by means of an impedance boundary condition defined by the normal impedance Zn(f) (Pas/m). The normal impedance is a complex-valued function that is function of the frequency.
• The normal impedance is related to the reflection coefficient R (complex ratio of reflected to incident pressure) as:
• The absorption coefficient, , is a real-valued quantity describing the amount of absorbed energy at a surface. It is related to the reflection coefficient as:
𝑍𝑛=𝜌𝑐1+𝑅1−𝑅
𝛼=1−¿𝑅∨¿2¿
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Absorbing and damping boundaries
• The surface properties are best described by the reflection coefficient or the surface impedance, as they contain both amplitude and phase information.
• Absorbing surfaces are often only characterized by their absorption coefficient (f). Because it has no phase information ( is unknown), this impedance is only an approximate description of the acoustic surface properties:
arbitrarily setting 0 will result in a real-valued impedance. This is NOT the fully correct description and may result in erroneous results. The importance of the phase decreases with increasing frequency.
• In the model, the absorption coefficient (f) of the different materials is defined by means of various interpolation functions under Global Definitions and we crudely assume 0.
𝑍𝑛=𝜌𝑐1+¿𝑅∨ ¿1−∨𝑅∨¿with|𝑅|=𝑒𝑖 𝜃√1−𝛼 ¿
¿
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Modeling Interfaces
• The “Pressure Acoustics, Frequency Domain“ user interface is used to perform Eigenfrequency and Frequency Domain studies.
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Modeling Interfaces
• A “Normal Acceleration“ boundary condition is used to define the sources.
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Modeling Interfaces
• “Impedance“ boundary conditions are used to define the different materials.
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Modeling Interfaces
The reflection coefficients and the normal impedances are calculated according to these expressions:
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Modeling Interfaces
The absorption coefficients of the materials are defined by means of interpolation functions which contain the alpha of each material vs. Frequency from 125 Hz to 4000 kHz.
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Modeling Interfaces
• A “Sound Hard Boundary (Wall) “ boundary condition is used for the remaining boundaries.
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Mesh and Solver Settings
• In acoustics, the computational mesh must resolve the acoustic wavelength. The requirement is to have at least 5 second order elements per wave length.
• The maximal mesh size is given by:
• The mesh size is defined under:Global Definitions > Parameters
h𝑚𝑎𝑥=𝜆5
=𝑐5 𝑓
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Mesh and Solver Settings
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Mesh and Solver Settings
• For large acoustic models it is efficient using an iterative solver with the geometric multigrid pre-conditioner.
• Decrease the relative tolerance (also lower than shown here) to get a more converged solution. This is important for higher frequencies with many standing modes.
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Results – EigenfrequencyAcoustic Pressure (acpr)
f = 72 Hz f = 77 Hz
f = 80 Hz f = 83 Hz
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Results – EigenfrequencySound Pressure Level (acpr)
f = 77 Hz
f = 80 Hz f = 83 Hz
f = 72 Hz
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Results – EigenfrequencyAcoustic Pressure, Isosurfaces (acpr)
f = 77 Hz
f = 80 Hz f = 83 Hz
f = 72 Hz
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Results – Frequency sweepAcoustic Pressure (acpr)
f = 200 Hz
f = 300 Hz f = 400 Hz
f = 100 Hz
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Results – Frequency sweepSound Pressure Level (acpr)
f = 200 Hz
f = 300 Hz f = 400 Hz
f = 100 Hz
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Results – Frequency sweepAcoustic Pressure, Isosurfaces (acpr)
f = 200 Hz
f = 300 Hz f = 400 Hz
f = 100 Hz
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Results – Frequency sweepSlice
f = 200 Hz
f = 300 Hz f = 400 Hz
f = 100 Hz
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Results – Frequency sweepIntensity
f = 200 Hz
f = 300 Hz f = 400 Hz
f = 100 Hz
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Results – Frequency sweepResponse
LeftCenter
Right
A Cut Point 3D data set is used to plot and evaluate a value at these points which would correspond to the audience.
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Results – Frequency sweepResponse
Resonance peaks are clear and due to the losses at the impedance boundaries.