Dedicated Acoustics Plots for Postprocessing
Dedicated acoustics postprocessing functionality exists to plot responses, transfer functions, sensitivity curves, directivity and radiation patterns, and more. They require the Acoustics Module license.
In this section:
Radiation Pattern/Bubble 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, the radiation pattern, or radiation bubble. 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. The plot can readily also be used to evaluate the results obtained with the The Pressure Acoustics, Boundary Elements Interface.
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 Beamwidth of the plotted data. The data is stored in a table that can be plotted using the Table Graph option.
Figure 2-9: 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. You can specify a separate expression for the surface color by deselecting the Use as color expression checkbox. A classical bubble plot is created by setting a constant value for the Expression field and using the sound pressure level for the color expression. 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). Note that this definition of the directivity can deviate from other standard formulations (see Ref. 6), if the radiation pattern is not plotted for all directions or if the main lobe is not on-axis.
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. For results from The Pressure Acoustics, Boundary Elements Interface the variables pabe.Lp or pabe.p can readily be used in the plot.
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.
The resulting radiation bubble can be exported to a .txt file for easy use in a subsequent Ray Acoustics model using the Radiation Pattern (Export) node. The data can then subsequently be used in the Source with Directivity feature.
In a 3D Radiation Pattern plot, the definition of the polar angle θ and the azimuthal angle φ follows the spherical coordinate system (r, θ, φ) typically used in physics.
Polar angle θ: acos(z/sqrt(x^2+y^2+z^2))
Azimuthal angle φ: atan2(y,x)
Bessel Panel: Application Library path Acoustics_Module/Tutorials,_Pressure_Acoustics/bessel_panel.
Loudspeaker Driver in a Vented Enclosure: Application Library path Acoustics_Module/Electroacoustic_Transducers/vented_loudspeaker_enclosure
Radiation Pattern and Results Analysis and Plots in the COMSOL Multiphysics Reference Manual
Radiation Pattern (Export) and Results Analysis and Plots in the COMSOL Multiphysics Reference Manual
Grid and Parametric Datasets
Another way of evaluating and depicting the exterior field is by using either the Grid 2D , the Grid 3D , the Parametric Curve 2D and Parametric Curve 3D, or the Parametric 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 2-10: 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.
Absorptive Muffler. Application Library path Acoustics_Module/Automotive/absorptive_muffler
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 2-11: 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