Tools for studying speaker directivity

Online speaker directivity simulators:

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 speaker with a cone diameter of 10 cm built into a wall radiates in all directions with the same intensity up to 1 kHz (constant directivity and sound power). From 1 kHz the intensity of radiation gradually decreases off-axis (increasing directivity, decreasing sound power). Increasing directivity is a consequence of destructive interference: at high frequencies sound waves radiated from different parts of the cone are cancel each other.

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 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 1.02

Software platforms: Excel | OpenOffice | LibreOffice

This Excel workbook displays the far field polar response of a theoretical cone speaker mounted in an infinitely large baffle. In the simulation all parts of the speaker vibrate in phase and with the same amplitude, and the speaker is completely flat.

The input parameters are the diameter of the cone and the frequency. In the polar graph the normalized sound pressure level is shown as a function of the angle at the selected frequency.

Speaker Polar Chart Display

Version: 1.02
Format: xls (Microsoft Excel 2003 Workbook)
Required software: LibreOffice Calc | Microsoft Excel | OpenOffice Calc
License: freeware

Speaker Directivity Simulator 1.03

Software platforms: Excel | OpenOffice1 | LibreOffice1

This Excel workbook displays the far field directivity of a theoretical cone speaker 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.

Note: above a certain frequency the directivity calculated from the rigid piston model is different from the directivity of real cone speakers 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

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

Acoustical simulation (all software)