Speaker Directivity Modeler

May 12, 2023

Speaker Directivity Modeler displays the far field frequency response of a circular rigid piston (which is a simplified, theoretical model of cone speakers) 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.

In the simulation all parts of the speaker vibrate in phase with the same amplitude and the speaker is completely flat. Cone resonances, high-pass filter behaviour, low-pass filter behaviour are excluded from the model.

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").

Validity of the model: 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.

Speaker Directivity Modeler

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 close to the loudspeaker, the frequency response corresponding to the selected angle matters. However, as we move away from the loudspeaker then the frequency response will gradually turn into the sound power response.

Sound power calculation for polypropylene or paper cone speakers with linear frequency response is valid up to ka=2. This frequency corresponds approximately to the frequency where the sound power response is -3 decibels. Above that frequency the real power response is less steep than the calculated version.

Radiated sound power vs. frequency is similar to the diffuse field response. This means that we can measure the sound power vs. frequency by measuring the diffuse field response in a reverberant chamber. The only difference between the two is that the power response is fixed, while the diffuse field response will be shifted up or down depending on the distance.

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