https://sites.google.com/site/undefi...diysunflowers
Paul Carmody has some insight into the open back midrange design.
Under "Crossover Design"
He mentions and describes a dipole "Peak" that boosts the sound at a certain dimension of the baffle versus frequency.
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Inches to Ohms
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O.K.
May we say ?............. ( f 3 not f c ) :
f3 = 4560 / WB ............ ( where WB = width of the baffle in inches )
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You are just playing a numbers game because you assume you have a circular baffle with diameter, in inchers, is the same magnitude as the resistance.
fc = 13500 / d
fc = 1 / ( 6.28 * r * c )
c = 1/ ( 6.28 * r * fc)
c = d / ( 6.28 * r *13500)
That is the correct equation.
Look at units.
c = inches / (6.28 * ((volts *sec) / coulombs) * inches / sec) = coulombs / volt = Farads.
If you let the magnitude of r equal the magnitude of d, yes, the magnitudes will cancel, but not the units. It is not ohms to inches. Additionally, this is not the cut off frequency. It is the frequency of the first peak in the dipole response which, as I posted earlier (post #6), is fc of a 1st order filter, with 10 dB gain, which will match the roll off of the dipole in the 6db/octave region. Additionally, what you are calling fc in post #10 is not the cut off frequency. It is the frequency at which the dipole axial response is at the same level as the monopole sources would be.
See my old web pages.
http://musicanddesign.speakerdesign....n_baffles.html (Don't confuse "d" on the web page (distance between sources) with diameter.
http://musicanddesign.speakerdesign....woofer_eq.html
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O. K .
For those less optimistic about open baffle behavior .
It is still possible to convert Ohms to inches .
fc = 13500 / d
fc = 1 / ( 6.28 * r * c )
13500 / d = 1 / ( 6.28 * r * c )
let r = d
13500 / d = 1 / ( 6.28 * d * c )
13500 = 1 / 6.28 * c
1 / 13500 = 6.28 * c
c = 1 / ( 6.28 * 13500 ) = 1 / 84780 = 11 . 8 uF
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This table shows the relationship between baffle diameter (in metres) and the
cut off frequency Fc. Below this frequency output will fall by 6dB per octave
until the driver resonance is reached when the slope changes to 18dB per
octave. For a circular baffle there will also be a peak where front and rear
radiation become coincident, shown here as Fp. There will also be further
peaks at multiples of Fp which is why, in general, circular baffles
should be avoided!
Per an accepted expert and guru :
Method of Calculation : From a given driver’s Thiele / Small parameters, the SPL/watt/m can be determined. For example, a typical 8 inch diameter midbass might be listed by the manufacturer as being 90 dB efficient. Manufacturers typically measure their driver’s response in 2π space using a very large baffle. If the same driver were placed in a typical rectangular enclosure and mounted in free space, the measured efficiency for the driver below the baffle step transition would be 84 dB (90 dB – 6 dB). The efficiency would then increase to 90 dB as the baffle step phenomenon comes into play for the midrange and high frequencies. The frequency midpoint of this transition from 4π space to 2π space can be estimated using the following relationship.
f3 = 4560 / WB where WB = width of the baffle in inches
Correcting for the baffle step loss at low frequencies can be handled in several ways. One solution would be to extend the baffle width WB to a very large value pushing the transition frequency below the systems operating range. This would lead to an extremely large baffle with no loss in driver efficiency. A second method would be applied in a two way design by placing the crossover point in the baffle step transition region and padding down the SPL output from the midrange driver and/or the tweeter driver. A third method is to apply a passive filter between the amplifier and the driver as shown by the schematic in Figure 3 at the top of the following page. I have used the third method in all of my full range speaker designs and found it to be a very simple, elegant, and powerful tool for rebalancing the SPL response across the entire frequency range.
Our differences in formulas my be due to ' pi space ' being considered ?
I don't think most rooms are whole space .
https://www.trueaudio.com/st_spcs1.htm
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Originally posted by hitsware2 View Post> Actually, for a circular baffle the low frequency response follow that of a 1st order high pass with Fc = C/D,
> and a gain of 10dB, where C is the speed of sound and D is the diameter.
More precisely ( since sound is circular )
( for Hz ) C = speed of sound in inches / second
Fc = 13500 / ( pi * diameter )
or :
Fc = ( 13500 / pi ) / diameter = 4299 / diameter
No.
Fc = C/D. C is about 1100 FPS or 13200 inches/sec
Fc = 13200 / D where D is in inches.
Also, in you original post you can't simply replace D with r. There is no such thing as an 8 inch resistor. You can compute Fc from the correct equation, above, and the find c as c = 1/(2 Pi Fc r) where you would chose r as desired. Or r = 1/(2Pi Fc c) where you would choose c as desired.
This has nothing to do with the character of sound other than it's speed and the propagation distance between the two dipole sources.
http://musicanddesign.speakerdesign....woofer_eq.html
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Originally posted by hitsware2 View Post> Actually, for a circular baffle the low frequency response follow that of a 1st order high pass with Fc = C/D,
> and a gain of 10dB, where C is the speed of sound and D is the diameter.
More precisely ( since sound is circular )
( for Hz ) C = speed of sound in inches / second
Fc = 13500 / ( pi * diameter )
or :
Fc = ( 13500 / pi ) / diameter = 4299 / diameter
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> Actually, for a circular baffle the low frequency response follow that of a 1st order high pass with Fc = C/D,
> and a gain of 10dB, where C is the speed of sound and D is the diameter.
More precisely ( since sound is circular )
( for Hz ) C = speed of sound in inches / second
Fc = 13500 / ( pi * diameter )
or :
Fc = ( 13500 / pi ) / diameter = 4299 / diameter
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> It is good perhaps to get a quick idea of the rough roll off of a baffle width.
Quick , and aurally ( within the realms of every day experience ) , accurate enough
for O . B . planning .
( As far as it goes ) ..... Next step is driver modeling .
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For practical purposes but I guess it is important to point out that the actual roll off of the dipole is much more chaotic than this implies and doesn’t factor baffle height or placement on the baffle.
Dont get me wrong, you are obviously smarter with math than I am, I just don’t want new people to rely solely on this to calculate their next OB build. It is good perhaps to get a quick idea of the rough roll off of a baffle width.
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Right .......... No valleys and peaks .
It shows what is relevant for practical purposes .
It is based on the math that was used for many
years to describe open baffle behavior .
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Interesting and certainly fascinating for someone like me who is not math savvy.
The main problem I see with this however is if it is open baffle I assume dipole, and it doesn’t account for dipole peak, which could cause several db of peaks and valleys, as well as a few hundred extra hz of low end extension.
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