Speaker Directivity Modeler

Room response calculation from radiated sound power:

May 12, 2023

Speaker Directivity Modeler displays the far field frequency response of a speaker driver with a flat, completely rigid diaphragm mounted in an infinite baffle. Since real speakers are not point sources, above a certain frequency the intensity of the radiation gradually decreases off-axis.

Speaker Directivity Modeler


Above a certain frequency the predicted response may differ from the response of real cone speakers. Cone break-up modes, propagation delay in the cone and cone geometry alter both on-axis and off-axis response.

Input parameters

The input parameters are the diameter of the cone and the angle of the listening axis. Angle of zero degrees is perpendicular to the baffle ("on axis").

Sound power curve

Sound power is the "total" radiated sound into full space (in our case, into half space due to the infinite baffle). The radiated sound power of speaker drivers decreases above a certain frequency. The cut-off frequency depends on the diameter of the driver and is independent of angle.

Sound power curve is important in closed spaces. On-axis response room response of a speaker driver is a combination of the sound power response (scaled according to room gain) and the on-axis response (a horizontal line for an ideal loudspeaker).

What do we hear? Frequency response corresponding to the selected angle or the sound power?

In free-field conditions (outdoor amplification) the frequency response corresponding to the selected angle matters and the sound power graph is irrelevant. In a reverberant room, the frequency response is a combination of the sound power curve and the curve of the selected axis. Close to the loudspeaker, the frequency response corresponding to the selected angle matters. As we move away from the loudspeaker, the frequency response curve becomes more and more similar the sound power curve.

Accuracy of the model - simulation vs. real cone speakers

The so-called piston model is valid up to the frequency of the first bending-wave resonance. This frequency depends on cone shape, cone material and cone diameter. Cone speakers also have a cone-surround resonance located between 1 kHz and 2 kHz, but it has minimal effect on directivity.

A brief study of cone resonances and their effect on frequency response and directivity: Geometrical Stiffness of Loudspeaker Cones (pdf, FINECone finite element analysis).

Note: often the off-axis response from 45° is a good estimate of the sound power response and the 20°-30° off-axis responses provide a good estimation of the room response.

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Acoustical simulation (all software)