Acoustic simulation tools to study speaker directivity



One of the most important features of loudspeakers and drivers is how their directivity (radiation pattern) varies as a function of frequency. For example, a 10 cm diameter speaker built into a wall radiates in all directions with the same intensity up to 1 kHz (constant directivity and sound power), on the other hand the intensity of the radiation gradually decreases off-axis from 1 kHz (increasing directivity, decreasing sound power). The reason for that the speaker is not an ideal point source and becomes directive at high frequencies due to destructive interference.

The simplest directivity model for cone speakers is the circular rigid piston mounted in an infinite baffle. While this is not the most accurate model, still a fair good approximation of real-life speakers up to a certain frequency. This frequency depends on the cone shape, material etc...

There are plenty of tools to display directivity: polar diagram (polar chart), DI (directivity index) vs. frequency, sound power vs. frequency, sonogram, parametric frequency response graphs.


Speaker Polar Chart Display 1.01

Software platforms: Excel | OpenOffice | LibreOffice

This simple simulation tool displays the far field polar response of a circular rigid piston (theoretical model of the cone speaker) mounted in an infinitely large baffle. The input parameters are the diameter of the cone and the frequency. In the polar graph the sound pressure level (SPL) is shown as a function of the angle.

The primary assumption in the analysis is that all parts of the piston vibrate in phase and with same amplitude, and the piston is completely flat. Above a certain frequency real cone speaker's directivity is different from that is calculated from the circular rigid piston model due to cone break-up modes, propagation delay in the cone and cone geometry.


Speaker Polar Chart Display

Version: 1.01
Format: xls (Microsoft Excel 2003 Workbook)
Required software: LibreOffice Calc | Microsoft Excel | OpenOffice Calc
License: freeware
Download




Speaker Directivity Simulator 1.03

Software platforms: Excel | OpenOffice1 | LibreOffice1

This simulation tool displays the far field directivity of a circular rigid piston mounted in an infinite baffle. The user can select from frequency response graph, 2D color map (sonogram) and waterfall plot.

In version 1.03 the simulation is extended with sound power and directivity index calculation, and additionally I made some visual improvements.

Note: above a certain frequency real cone speaker's directivity is different from that is calculated from the circular rigid piston model due to cone break-up modes, propagation delay in the cone and cone geometry.


Cone speaker (circular piston) directivity simulator

Version: 1.03
Format: xls (Microsoft Excel 2003 Workbook)
Required software: LibreOffice Calc1 | Microsoft Excel | OpenOffice Calc1
License: freeware
Download

Note: In OpenOffice Calc and LibreOffice Calc waterfall plot and 2D color map are not available.





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