# what is the equation to calculate driver beaming by diameter?



## kappa546 (Apr 11, 2005)

I know it's something along the lines of drivers begin to beam once the wavelength of the frequency played is shorter than the diameter of the driver, but i can't be sure. just wanted to double check, i can't seem to find it online.


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## kappa546 (Apr 11, 2005)

nevermind i found it. 

in case you were curious: speed of sound = 1145 feet per second at sealevel. 1145x12 = speed of sound in inches. then divide by the diameter of the drivers cone. 

ie: (1145x12)/3=4580. A 3" driver will begin to beam at 4580hz.


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## t3sn4f2 (Jan 3, 2007)

kappa546 said:


> nevermind i found it.
> 
> in case you were curious: speed of sound = 1145 feet per minute at sealevel. 1145x12 = speed of sound in inches. then divide by the diameter of the drivers cone.
> 
> ie: (1145x12)/3=4580. A 3" driver will begin to beam at 4580hz.


Npdang uses 4311 in one of his reviews.


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## mvw2 (Oct 2, 2005)

172000/Diameter(mm)

This will be the transition point between omni-directional and directional where off-axis begins to influence the response, i.e. beaming.

Some folks consider the beaming point 1 octave above this.

For example, a 6.5" woofer will transition from omni to directional around 1kHz. Some consider the beaming point to be around 2kHz as you won't really see much of a difference in dB from axis angle till then. It depends on how off-axis you run and how close in dB is not close enough. It might be that a particular 6.5" woofer will play within 2dB out to 3kHz between 0 and 45 degrees off axis. If you run them in this range and don't care about anything under a 3dB difference, you won't much mind crossing them up to 3kHz even though they technically become directional at around 1kHz. Now if you were 60 degrees off axis, that woofer may show a 5dB drop by 3kHz. So you do have to be careful with what you pick for x-over points for your particular install. If you don't, you pretty much have to fix the response with EQing, and this needs a separate left and separate right EQ to let you adjust what you need for the variation. As well, this only adjusts to the driver's seat. The passenger gets a messed up response. In the end, you try to cross lower if you need to or aim the drivers more on-axis so there's little to no issue in the first place.


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## Oliver (Jun 25, 2007)

In an anechoic chamber this should readily become apparent [ beaming ].

Have you ever banked a ball when shooting pool ? 

reflections, deflections , refractions, etc..,

Kinda like a pinball bouncing around , whoohoo!


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## michaelsil1 (May 24, 2007)

durwood said:


> I was trying to come up with a way to predict off-axis response or how a midrange driver will roll off at higher frequencies. I know all sorts of things can happen, but is there some general modeling that can be done based on wavelength of the frequency, cone diameter, and angle of the axis?
> 
> I know beaming can occur as the wavelength approachs the diameter of the cone. (wavelength at a given frequency = cone diameter)
> 
> ...


I did some searching and found these numbers; would you say they are accurate?


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## kappa546 (Apr 11, 2005)

The equation I got was from one of Abmolech's posts. sounds about right to me.


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## Oliver (Jun 25, 2007)

So lets take a component set...

where would you x-over these ?

6.5" ~ 2,120Hz = midrange ? [ how high should this speaker play to ?

How low should either of these be crossed at ?

2" ~ 6,880Hz = tweeter ? [ does this start on the low side at say ???? and then what on the high side ? ]


1" ~ 13,750Hz = tweeter ?


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## freeride1685 (Oct 3, 2007)

not to throw a stick in the spokes but how does beaming apply to ribbon tweeters? i have heard that they have exceptional horizontal dispersion but not vertical...i wonder if that vertical dispersion drops off in a similar way to the off axis response of a normal round speaker....maybe it correlates to the length of the ribbon?


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## SSSnake (Mar 8, 2007)

I think the 1145 you are referring to is ft/sec NOT ft/minute. Not trying to nitpick, just trying to put it out there so everyone understands why it works mathematically.


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## kappa546 (Apr 11, 2005)

SSSnake said:


> I think the 1145 you are referring to is ft/sec NOT ft/minute. Not trying to nitpick, just trying to put it out there so everyone understands why it works mathematically.


you're right... brain fart on my part. fixed.


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## kappa546 (Apr 11, 2005)

freeride1685 said:


> not to throw a stick in the spokes but how does beaming apply to ribbon tweeters? i have heard that they have exceptional horizontal dispersion but not vertical...i wonder if that vertical dispersion drops off in a similar way to the off axis response of a normal round speaker....maybe it correlates to the length of the ribbon?


It does correlate to the length of the ribbon for the same reason explained above.


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## Oliver (Jun 25, 2007)

freeride1685 said:


> not to throw a stick in the spokes but how does beaming apply to ribbon tweeters? i have heard that they have exceptional horizontal dispersion but not vertical...i wonder if that vertical dispersion drops off in a similar way to the off axis response of a normal round speaker....maybe it correlates to the length of the ribbon?


Beaming may be a physics phenomina [ hence the diameters of round surfaces ].

Some numbers for speed of sound 

quote>

the speed of sound is 343 m/s. This also equates to 1235 km/h, 767 mph, 1125 ft/s

quote>
http://en.wikipedia.org/wiki/Sound_speed


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## br85 (May 2, 2008)

If I listened correctly to my friend (old guy, friend of N. Thiele's), the beaming frequency can be increased in certain cone shapes by using a circular voice coil behind the surround somehow (I'm pretty sure aurasound does this with their small fullrange drivers). So if my memory serves me correctly, there are some exceptions to the beaming "formula".


*it might have been domes.


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