Dedicated Acoustics Plots for Postprocessing
Dedicated acoustics postprocessing functionality exists to plot responses, transfer functions, directivity patterns and more. They require the Acoustics Module license.
In this section:
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Radiation Pattern Plots (Spatial Response)
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Grid and Parametrized Datasets
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Octave Band Plots
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Directivity Plots
Radiation Pattern Plots (Spatial Response)
Evaluating and plotting the acoustic pressure around radiating objects and sources is essential for the development of several acoustic devices. This is known as the spatial response or the radiation pattern. Application areas range from underwater acoustic transducers and loudspeakers, to determining the spatial sensitivity of microphone systems (for example, using reciprocity). Using the Exterior Field Calculation feature can help to reduce the computational domain while still being able to determine the pressure and thus the spatial response in the exterior field (near-field to far-field). The Radiation Pattern plots are specially designed for easy evaluation of the exterior field variables, that is, the acoustic exterior pressure and the exterior field sound pressure level.
In the radiation pattern plots, the exterior field variable (pressure or sound pressure level) is represented in a polar plot for a selected number of angles. Data is retrieved on an evaluation circle in 2D, 2D axial symmetry, or 3D. The angle interval and the number of angles can be manually specified. The evaluation circle origin, orientation, and radius can be specified as well as the reference direction. The evaluation circle can be visualized using a Preview Evaluation Plane functionality. There is also a built-in option to calculate the Beam Width of the plotted data. The data is stored in a table that can be plotted using the Table Graph option.
Figure 2-7: Example of a 2D and 3D radiation pattern plot from the Bessel Panel tutorial model.
The 3D radiation pattern plots create a 3D polar plot (or bubble plot) where the data is evaluated on a sphere. Here, you can specify a separate expression for the surface color. In the 3D radiation pattern plots, the directivity can also be calculated by enabling the Compute directivity option. The result is given in a table and is calculated as the maximum power relative to the average power. The table comprises the maximal radiation direction (polar angles), the directivity, and the directivity given in dB (also known as the directivity index).
The main advantage with the radiation pattern plot, as compared to making a line graph, is that the circle/sphere that you use for defining the plot directions, is not part of your geometry for the solution. Thus, the number of plotting directions is decoupled from the discretization of the solution domain.
Variables defined by the Exterior Field Calculation feature like, for example, the pressure acpr.efc1.pext or sound pressure level acpr.efc1.Lp_pext are globally defined variables and can be directly evaluated in the Radiation Pattern plot and Directivity plot. The values plotted only make physical sense if they are evaluated outside of the Exterior Field Calculation boundary.
To visualize, for example, the sound pressure level inside of the Exterior Field Calculation boundary plot the expression: at2(x,y,acpr.Lp) in 2D, at2(r,z,acpr.Lp) in 2D axisymmetry, or at3(x,y,z,acpr.Lp) in 3D. The at2() and at3() operators ensure the variables are globally defined.
Default exterior field plots (that use the radiation pattern plots) are automatically added to any model that uses exterior field calculation feature, when Generate default plots is selected (the default) on the study node.
In a 3D Radiation Pattern plot, the definition of the polar angle θ and the azimuthal angle follows the spherical coordinate system typically used in physics.
To help visualize the angles, assuming the center is at the origin, simply plot the following expressions:
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Polar angle θ: acos(z/sqrt(x^2+y^2+z^2))
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Azimuthal angle : atan2(y,x)
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For a 3D example, see Bessel Panel: Application Library path Acoustics_Module/Tutorials,_Pressure_Acoustics/bessel_panel.
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For a 2D axisymmetric example, see Cylindrical Subwoofer: Application Library path Acoustics_Module/Tutorials,_Pressure_Acoustics/cylindrical_subwoofer.
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Evaluating the Acoustic Field in the Exterior: Near- and Far-Field
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Radiation Pattern and Results Analysis and Plots in the COMSOL Multiphysics Reference Manual
Grid and Parametrized Datasets
Another way of evaluating and depicting the exterior field is by using either the Grid 2D , the Grid 3D , the Parametrized Curve 2D and 3D, or the Parametrized Surface datasets. All of these datasets allow the evaluation of global quantities, like the exterior field variables, outside of the computational domain (outside of the mesh).
The exterior field is depicted in several ways in the model Piezoelectric Tonpilz Transducer: Application Library path Acoustics_Module/Piezoelectric_Devices/tonpilz_transducer.
Octave Band Plots
A dedicated Octave Band () plot exists to plot frequency response, transfer functions, transmission loss, and insertion loss curves. The plot has several built-in acoustics specific features like predefined weighting (Z, A, C, and User defined) as well as the possibility to plot the response in octaves, 1/3 octaves, 1/6 octaves, or as a continuous response.
Figure 2-8: Sensitivity curve plotted as 1/3 octave bands and a continuous curve. From the Loudspeaker Driver model in the Application Library.
For details see Octave Band in the Results Analysis and Plots chapter in the COMSOL Multiphysics Reference Manual.
The predefined Z, A, and C weightings are defined in IEC 61672-1. See IEC 61672-1 Electroacoustics - Sound level meters - Part 1: Specifications for details.
For examples that use an Octave Band plot, see:
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Absorptive Muffler: Application Library path Acoustics_Module/Automotive/absorptive_muffler
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The Brüel & Kjær 4134 Condenser Microphone: Application Library path Acoustics_Module/Electroacoustic_Transducers/bk_4134_microphone.
Directivity Plots
Another acoustics specific plot, especially used for loudspeakers, is the dedicated Directivity () plot. The plot allows audio engineers to depict the spatial response of a loudspeaker as function of both frequency and spatial angle in a contour-like plot. Representing the spatial response in this manner is a very common in the loudspeaker industry. Measured data is often also represented in the same manner. The plot includes many options to format the plot to achieve maximal insight into the modeled data, for example, linear and logarithmic frequency axis scaling options, easy switch of the x- and y-axis (frequency and polar angle axis), as well as options to normalize the data with respect to a given angle or the maximal value.
Figure 2-9: Example of the directivity plot from the Lumped Loudspeaker driver model in the Application Library.
 
For details see Directivity in the Results Analysis and Plots chapter in the COMSOL Multiphysics Reference Manual.
Lumped Loudspeaker Driver. Application Library path:
Acoustics_Module/Electroacoustic_Transducer/lumped_loudspeaker_driver