Speaker Directivity Modeler
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 driver has a flat, completely rigid diaphragm (all parts of the speaker vibrate in phase with the same amplitude, no cone resonances).
- Driver is mounted in an infinite baffle (half-space simulation, no diffraction from the baffle edge).
- High-pass filter behavior, low-pass filter behavior are not part of the simulation.
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.
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.
- Cone break-up region of speakers with curved and shallow paper or polypropylene cone starts at around a frequency where the simulated sound power response drops by 3dB. Above that frequency the off-axis behavior is different from the rigid piston model. These speakers provide the widest dispersion for a certain diameter.
- Cone break-up region of speakers with straight or slightly curved paper or polypropylene cone begins at a higher frequency (approx. twice the frequency of the -3dB drop in the simulated sound power response). Measured sound power response is less steep than the calculated, probably due to the limited wave propagation velocity in the cone.
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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