Dispersioin of cones

[stevem]

Does anyone know if there is a way to determine the dispersion angle for a cone driver at various frequencies? For instance, I am trying to determine what the dispersion of a 10 inch cone midrange at 1200 Hz is. Any help is appreciated. Thanks.

[johnaec]

Look at this document to see the 45 degree off-axis curves for the 10" 2012H. Since you're dealing with similar physics in most 10" speakers, they should be fairly similar: http://www.jblpro.com/pages/pub/components/2012h.pdf

John

[Dougie]

You can't really judge the dispersion angle of one driver at different frequencies and assume that all 10'' drivers are the same, or close to. They are all different. The only way to tell accurately is make a polar plot which requires the proper measuring equipment. A lot of speaker manufacturers today publish polar plots for their products.

Doug

[ralphs99]

Hi Steve,

While what is Doug is saying is true, it is possible to generalise about the dispersion angle of a driver if that driver behaves as a piston, ie without cone breakup. Once breakup occurs, or if the driver is fitted with auxilliary radiating devices such as whizzer cones, those generalisations fall down and dispersion becomes wider than predicted. But for a good quality 10" midrange it's fair to assume that it will be operating as a piston at 1200Hz. So to answer your question, a 10" driver with an effective cone diameter of about 8" will have it's -6dB points at about +/-70 degrees on axis. Additionally you can expect +/-50 degrees at about 1700Hz and +/-18 degrees at 3400Hz.

The best way to find out for sure, as Doug points out, is to examine the polar plots for the driver in question.

Cheers, Ralph

[stevem]

Thanks guys, I appreciate the help. I am actually using the 2012H driver, but I can't find the polar plots for it. Are they published anywhere? I'm trying to see what the best dispersion pattern horn would be to mate with it at 1200hz.

[whgeiger]

SM,

We may model a direct radiating loudspeaker as a rigid circular piston mounted in an infinite baffle. Here the pattern of radiation into a single hemisphere is addressed to a first order approximation. For this purpose, the effects of Fresnel diffraction, those attributable to cone geometry and breakup, as well as those related to enclosure size and geometry may be ignored.

Given

[a] – piston radius (m)

[c] – sound velocity in free air
= 345 m/s

[f] – frequency of interest (Hz)

[t] – beam-width (included) angle for –3dB points

= 2 * arcsin (0.255*[c]/([f]*[a]))


Note that for argument values > 1, the arcsine function is undefined. Note also for a 10” driver [a] = 0.1 m (approx). Thus, for [f] < 0.255 * [c]/[a] = 880 Hz. the –3dB beam-width [t] does not exist.

From these observations, it may be concluded that such a driver radiates a ‘beam’ that is no more than 3 dB down in any direction 90 degrees from the principal axis for frequencies 880 Hz or less. Above this frequency, beam narrowing may be calculated from the formula given above.

Regards,

WHG

[johnaec]

You might look up info on some of the larger studio monitors that used 10" midrange speakers - there were quite a few. None of them were the 2012H, but this will probably give you a good starting point.

I've got a pair of 2012H's I'm putting into a system, but I'm crossing over to the 2105H, not a horn. I may throw one of them in a cabinet for testing if I can talk Mr. Widget into running it through his Clio system sometime...

John

[ralphs99]

Thanks for the exact formula WHG.
The only other comment I would make concerns the effective radius. I looked at the Sd value published by JBL under the TS parameters for their 10" drivers. All are listed as 0.032m sqaured. Do you feel the radius thus derived is the most appropriate value to use in the formula? I am surprised that the different 10"ers with their different suspension types all have the same value for Sd.

Cheers, Ralph.

[whgeiger]

Thanks for the exact formula WHG.
The only other comment I would make concerns the effective radius. I looked at the Sd value published by JBL under the TS parameters for their 10" drivers. All are listed as 0.032m sqaured. Do you feel the radius thus derived is the most appropriate value to use in the formula? I am surprised that the different 10"ers with their different suspension types all have the same value for Sd.

Cheers, Ralph.

Ralph,

Some notes follow:

[1] Driver effective piston size is sufficiently characterized by radius [a] in this setting.

[2] Note that [a] = ([Sd]/[pi])^(1/2).
For a 10” driver where typically [Sd] = 0.032 m^2,
[a] = (0.032/3.14159)^(1/2) = 0.1 m

[3] The effective (projected) radiating area [Sd] includes the inner part of the surround that moves with the cone. Only at the outer edge, where the surround is attached to the driver frame, is no movement (air displacement) taking place.

Regards,

Bill