[FlorianO]

Hello all,

I just wanted to double-check some distinction wrt. dipole Fequal (as e.g. in flat OBs) vs. F(3) baffle diffraction step in _enclosures_

Fequal
~~~~
- Definiton: The frequency were the dipole output (+6dB more than monopole at the top) becomes equal with monopole i.e. O dB.
- Sources: Linkwitz site (primarily), cited (sometimes wrongly) in several places.

Fequal = 0.17*v/D or, alternatively 58.31 Hz/D, where D is the (metric) path difference btw. back wave and front wave. For a flat OB that is the difference from the cone center to baffle edge.

For an 1 m wide baffle that corresponds to 116 Hz. 

F(3)
~~~
* Baffle diffraction step in __enclosures__
* Sources: Olson Acoustic book interpretation by John Murphy  (at hisTrueAudio site):

 f(3) = 115/W(B)
(where W(B) is the baffle width in meters)


Confusingly enough, we end up with same numbers for two different things. Is my above understanding correct ? Are the (almost) exact same numbers just a coincidence ?

I've seen several places where they are (seemingly) confused. For example Dick Olsher original review of Visaton NoBox speaks about the "cutoff frequency"  in the context of an Open Baffle...

 

[MJK]

I suggest that you model a baffle with a driver in the EDGE program. You can flip between a closed box and an open baffle configuration and watch the plotted baffle response change. Compare the frequency response with the predicted f3 from the appropriate formula and see how well the rules of thumb hold up for different baffle geometries. The best way to learn is by doing, you will gain a much better understanding and intuitive feel.

[JohninCR]

Florian,

Yes with a flat baffle they achieve a very similar result, because they have the same cause, waves bending around the baffle edge as they transition from only a half space wave launch to full space expansion.  The baffle step method is the one Hitsware uses.  I go with Linkwitz because it is applicable to any shape or folding even U-baffles.  It's a good starting point, but you have to keep in mind that it's a free space result and boundaries have a significant impact.

Like Martin said, programs like the Edge are useful too, for flat baffles, because it predicts response based on some baffle shapes and the driver positioning on the baffle

[FlorianO]

Ah, yes.  That's why it is actually called "step" i.e. when the sound goes "Aaaaaa..." as it  falls off the baffle with 3 dB from 2 pi steradians to 4 pi steradians 

Thanks Martin, John.


P.S: Edit:  Yes, of course it is half i.e. 6 dB, not 3. Sorry for that, hands were faster than brain there

[MJK]

falls off the baffle with 3 dB from 2 pi steradians to 4 pi steradians

Actually 6 dB.  Again, I strongly recommend trying the EDGE software.  Discussing on a forum will not get you to the level of understanding that spending a few minute messing with the software will provide.

[Dougl]

I agree that a baffle Sim will be more educational than anything else.

BTW:  Your definition of D is subtly wrong.  D is NOT the width of the baffle.
D is the Diameter of the circle that has an area equal to the area of the baffle.

An example of this, a Square 24" baffle would have a smaller D than a 48 H, 24 W baffle.

I'll try to come up with numbers after work.

Hope this helps;

Doug

[JohninCR]

Actually D is the Differential in the travel distances of the front and rear waves to the listening position.  eg for a circular baffle "D" is the radius.  There are a number of complicating factors as well.  While in free space a driver centered on a 48"H x 24"W flat baffle is going to have better bass extension than one 24"x24", in normal usage with the bottom edge on the floor the 24"x24" will outperform the larger baffle, because the effect of the floor is greater in terms of baffle boundary and the driver is closer to the floor too.  While the floor effect in terms of boundary reinforcement is quantified at +6db, I've never seen it quantified in terms of the effective baffle.  Maybe some of the modelling programs can do so.  I approach it in terms of typical engineering and allow plenty of cushion by expecting less and and getting more.  Then the woofer(s) are less stressed at high SPL resulting in lower distortion. 

edit-  Sorry Doug, I didn't realize you were talking about the baffle step formula.

[johnk...]

Fequal is defined where the front and rear waves are 120 (or 240)  degrees out of phase. The vetcors  of the front, rear and summed result form an equilateral triangle. Since they start at 180, an additional rotation of 60 degrees is requires which comes when the 6 times the effective separation of the frequency is F = C/(6d), where C is the speed of sound and d is the separation. Often written as F = 0.17C/d (Hint, 1/6 = 0.16666666...  or approximately 0.17).

[FlorianO]

While the floor effect in terms of boundary reinforcement is quantified at +6db, I've never seen it quantified in terms of the effective baffle. 

In his original  Visaton NoBox review Dick Olsher quotes a paper* where that factor is sqrt(2).  I.e. a 168 cm wide flat OB (half wavelenth at 100 Hz) is reduced to 119 cm. Again, apparently saying "cutoff frequency" while meaning Fequal,  but still.

Don't have access to that paper to double check.

Florian

P.S. Will d/l EDGE and play w/  it. I can forsee a very productive Friday at work....

*: paper:  (unknwon title), Raymond Newman  (AES Journal, Vol. 28, No. 1/2, 1980).

[FlorianO]

Fequal is defined where the front and rear waves are 120 (or 240)  degrees out of phase. The vetcors  of the front, rear and summed result form an equilateral triangle. Since they start at 180, an additional rotation of 60 degrees is requires which comes when the 6 times the effective separation of the frequency is F = C/(6d), where C is the speed of sound and d is the separation. Often written as F = 0.17C/d (Hint, 1/6 = 0.16666666...  or approximately 0.17).

Thanks John, highly appreciated. Always wondered where does that 0.17 come from. Quite some time since I've last dealt with phasors...

[JohninCR]

JohnK,

Thanks for the detail, I like to learn something new every day.  I was under the false impression that it was at 90deg or 270deg for the rear wave to neither reinforce nor cancel the front wave.  The reasoning is going to take some brain crunching....180 totally cancels, 0 totally reinforces, so why wouldn't 90 leave just the front wave and equal to a monopole?  I must be missing something.

[FlorianO]

Due to the perpendicular phasor summation. At 90 degrees the summed response will be sqrt(2) times the front phasor i.e. (still) +3dB up.

It's not linear, John...

[JohninCR]

I'll just leave the math to you guys, and decrease my rule of thumb from 58.3h to 57.2hz for a 1m "D" using the more precise .1667 in the formula assuming 343m/s speed of sound, which is reasonable given my elevation and typical temperature.  I'll just have to accept that I get a little less bass during rainy season due to the increased humidity.

[scorpion]

John,
I really like your last post here. But isn't it time that we introduce The Earth Crisis Climatic Conditions also into our Hi-FI World ! 

/Erling

[JohninCR]

John,
I really like your last post here. But isn't it time that we introduce The Earth Crisis Climatic Conditions also into our Hi-FI World ! 

/Erling

I think my speakers and I can handle +1 to +2deg C over my remaining lifespan.  Worst case I'll have to give back that 1hz that JohnK gave me.  About the only thing that could affect me would be a climate shift that stopped the rain, because except for a few windmills CR is 100% hydroelectric.  A tank of gasoline lasts me about 2 months, so I'm doing my part.

[FlorianO]

A tank of gasoline lasts me about 2 months, so I'm doing my part.

Except you they are cutting a lot of wood for your speakers. So, pls put them on a container and ship them to Sweden (incl. the speaker drivers, thank you). I honestly promise I will recycle them here

 

[JohninCR]

A tank of gasoline lasts me about 2 months, so I'm doing my part.

Except you they are cutting a lot of wood for your speakers. So, pls put them on a container and ship them to Sweden (incl. the speaker drivers, thank you). I honestly promise I will recycle them here
 

As they say where I'm from "that dog don't hunt", forestry management is big here and the trees will grow back.  It's the people willing to pay $12,000 per cubic meter for mahogany and the exotic veneers available in the developed world that cause tree poaching.

[Dougl]

Actually D is the Differential in the travel distances of the front and rear waves to the listening position.  eg for a circular baffle "D" is the radius.  There are a number of complicating factors as well.  While in free space a driver centered on a 48"H x 24"W flat baffle is going to have better bass extension than one 24"x24", in normal usage with the bottom edge on the floor the 24"x24" will outperform the larger baffle, because the effect of the floor is greater in terms of baffle boundary and the driver is closer to the floor too.

I agree with your statements.  However, if you take your 24" square baffle with the driver centered, and add a 24" square baffle above it, D is going to increase by the Square root of 2.  D' = D(Squ(2)) Where D" is the 24 * 48 D.

This should allow for about a half octive deeper base, without any real penelties.

Doug

[johnk...]

Actually D is the Differential in the travel distances of the front and rear waves to the listening position.  eg for a circular baffle "D" is the radius.  There are a number of complicating factors as well.  While in free space a driver centered on a 48"H x 24"W flat baffle is going to have better bass extension than one 24"x24", in normal usage with the bottom edge on the floor the 24"x24" will outperform the larger baffle, because the effect of the floor is greater in terms of baffle boundary and the driver is closer to the floor too.

I agree with your statements.  However, if you take your 24" square baffle with the driver centered, and add a 24" square baffle above it, D is going to increase by the Square root of 2.  D' = D(Squ(2)) Where D" is the 24 * 48 D.

This should allow for about a half octive deeper base, without any real penelties.

Doug

 At low frequency any shaped baffle can be shown to be equivalent to a circualr baffle with driver centered of some radiushttp://www.musicanddesign.com/Equivalent_Baffles.html. For a 24" x 24" baffle with centered driver at 12" x 12" the equivalent circualr baffle has a diameter of about 27". Extending the baffle to 48" tall, but keeping the driver at 12" x 12" yields an equivalent diameter of 35'". Placing either baffle near a floor will result in a 4Pi to 2Pi transition which will boost the low frequency response by about 6dB below nominally 100 Hz. The 6dB "floor" boost for the smaller baffle at low frequency is greater than the gain from the larger baffle in free space as the larger baffle only yields a 2.25dB  boost over the smaller baffle in free space.

[scorpion]

johnk,

Your web is growing into a well of valuable knowledge for the OB/dipole community,

Thank You !

/Erling