Speaker Cone Diameter v Radiation Pattern

http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/cirapp2.html#c2

 

http://greenboy.us/fEARful/frequencytables.htm

 

OP, I don't have the link on my phone but Greenboy's site has a reference chart somewhere.

A direct radiating ("normal" way you see speakers made. Not horns or bandpass boxes or multiple speakers stacked certain ways) speaker starts to become directional at the frequency where to effective cone diamer is one either full, or 1/4 wavemength across, can't remember which but full wavelength makes more sense. This is assuming a speaker is acting like a piston, which it does not outside of the lower frequencies.

Some rough guesstimates of where various speakers start to beam, which I'm using to mean losing spread inside of a 90 degree arc in front of the cab.

18".......600-800hz

15".......1khz

12"......1500hz

10.....2khz

8"......2500hz

6".....3khz.



Rough estimates there.



One rule of thumb for designing multi-way speakers (but certainly not the be-all/end-all design) is to crossover to the next higher speaker at whatever the lowest frequency is where the lower speaker reaches -6db @ 45 degrees off axis (the 90 degree arc in front of the cab).

 

http://www.acs.psu.edu/drussell/demos/baffledpiston/baffledpiston.html

 

Side by side speakers share the beaming of a single driver of the combined arrangement's width.

 

Keep in mind that a speaker does not act like a piston at all frequencies, but rather inly in the lows.

On a phone here, so once again, I shall rely on Passinwind to post link to these vool appelets that animate such things as waves moving from the coil (dustcap) outward and the fact that the dome (center) of the speaker and its outer edges can in fact be moving different directions and technically be 2 different radiators when asked to move back and forth really fast (higher frequencies) and this will show the non-piston behaviour and thus the fact that you can't just calulate diameter/frequency. Sometime in the 1970's, Altec tried to take advantage of this by designing a speaker where the middle dome "tried to act like" a radiator seperate from that of the rest of the woofer, thereby creating 2 radiators in one cone. A smallsr one in the center (high freq.) and a lower one in the rest of the cone (lower freq.). Similair to how a coax aorks but without the different parts.

Like anything, it was yet another balance of tradeoffs...etc. If you habe a cone that is pliable/soft enoigh to allow "waves" to go through it on the order of what it would take to let the center portion act as a separate entity from the outer portion...you woulxn't be able to optimize either, just make them the best they can be witthout neutering the other.

 

Sorry if that easn't all that clear an explanation. ^^

I got interrupted like 3 times and stumbled over my own feet probably twice.

 

There's one man who perfected this, the late Jim Thiel.
He designed a small driver that's actually a coaxial/coincident driver with one motor. The voice-coil is directly attached to the dome to get the best high frequency reproduction possible, the dome is then attached to the 4"cone via a special surround. The stiffness of that surround determines the frequency from which only the domes radiates high frequency. This is a very unique system but when executed well it is one of the best point-sources available

 

That's pretty neat, hadn't read up on that one.


For some dumb reason Talkbass started turning all dark blue when I log in. Harder than hell to read anything here on a phone.

 

With the sort of speakers found in bass cabs (large diameter drivers with relatively low moving mass) they go non-pistonic from a few hundred hertz upwards. This means that the simplistic beaming calculations which assume pistonic behaviour mean basically nothing.

Smaller drivers will tend to have better off-axis response, just as larger drivers tend to be more sensitive, but it comes down the minutiae of voice coil and former, cone, dustcap, surround and even the glue joints, as to how the response actually is off-axis. It's certainly possible to design a 15" with better off-axis response than some 10"s. I've spent a lot of time on this over the last couple of years and it's remarkable what a complex interactive puzzle it is.

AES3192, "Design Parameters and Trade-Offs in Large Diameter Transducers" by Doug Button of JBL is very interesting reading on this matter and many others which relate to bass cabs.

 

This happens with whizzer cones but in a much messier way because of the whizzer's undamped break-up nodes. It also happens with conventional dust-caps as well as with ones connected directly to the voicecoil former, although not as neatly as those with a direct connection. The flexible joint between the voicecoil+dustcap assembly and the main cone acts as a mechanical crossover, with a resulting phase shift and this notch at the crossover frequency because the phase can't be corrected through reversing the polarity with which the dustcap is driven (as you'd do with a lot of electronic tweeter crossovers).

If you can get the cone's radiating area to shrink inwards at higher frequencies, thanks to the non-pistonic flexure of the cone, and use the surround to damp the higher frequency output of the outer region of the cone then you can get much better off-axis response from the cone itself than you'd expect. Then get the dustcap+voicecoil assembly right and it'll go higher still with good off-axis response. Thankfully it's not quite as trial and error a process as it used to be but it's still more empirical than most bits of loudspeaker design.

 

And speaking to what Alex just said, I've heard quite a few people on here say that the Faital 15PR400 has better off-axis dispersion than any other 15" they've used. Not familiar with it personally, but these are opinions of people who know their stuff. So yeah, Alex makes a point

 

I can't find the links now, but there are some animations out there that would help people visualize this stuff.

There is a bit of a "pebble in the pond" ripple effect from the center of the cone outwards. So, as these guys are saying, if they can bring all this into a balance, the dustcap can act like more of an independent small diameter radiator, thereby increasing dispersion, like smaller speakers do.

 

There are a few here.

 

This poster is good too, though no animations: http://www.klippel.de/fileadmin/kli...ture/Papers/KLIPPEL_Cone_Vibration_Poster.pdf