# Tools for studying 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 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.

Online simulation is also available at the following link.

Online Speaker Directivity Modeler »## 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.

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 | OpenOffice^{1} | LibreOffice^{1}

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.

Format: xls (Microsoft Excel 2003 Workbook)

Required software: LibreOffice Calc

^{1}| Microsoft Excel | OpenOffice Calc

^{1}

License: freeware

Download

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

## About the accuracy of the model

As the speaker becomes more directional (starts to 'beaming') with increasing frequency, the difference between the output of the rigid piston model and the normalized off-axis measurements of cone speakers becomes greater. If the maximum allowed deviation from the measured response is 2 dB (the measured off-axis response is normalized to 0 deg), then the high frequency limit of the flat piston model for cone speakers:

- Between 0° and 30° the simulation is accurate up to
*ka*=4. - Between 30° and 60° the simulation is accurate up to
*ka*=3. - Between 60° and 90° the simulation is accurate up to
*ka*=2.

(The value of *ka* is calculated and displayed.)

Simulation vs. measurement with an example: the graph below shows the simulated response of a 6.2 cm speaker (D = 6.2 cm, S_{d} = 30.2 cm^{2}) from 30° off-axis and the normalized off-axis response of the Dayton Audio PC83-4 3" full range speaker from 30°. The speakers have the same effective cone area.

See also:

Speaker Directivity Modeler (online)

Room Boundary Simulator (Windows)