The Golden Rule?

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Has anyone ever heard of the Golden Rule in speaker box building? I heard something about this and the formula is supposed to be 0.6 x 1.0 x 1.6 I am not sure what the multiplier is but I figure these three numbers are the height/width/depth when multiplied by another number. Could someone please help me with this one. I am going to be building a home theater system and need to figure out what size box I am going to need. The big question is If I am going to be putting two Tang Band W3-881S into one enclosure what size does the inside measurments need to be for each speaker? If possible I would like to keep the depth around 4" and the enclosure taller than wider. Going for the slimmer look. Thanks for any advice that comes my way.

Jered22
 
jered22 said:
... I heard something about this and the formula is supposed to be 0.6 x 1.0 x 1.6 I am not sure what the multiplier is but I figure these three numbers are the height/width/depth when multiplied by another number...
Jered22


It is the "Golden Ratio". When a speaker box is built with its dimensions in this ratio internal standing waves are (supposed to be) minimized. So the numbers themselves are the multipliers.

If your width for instance is 6 inches then the depth would be 10 inches and the height would be 16 inches. It actually doesn't matter with dimension is the height, width or depth.
 
So if this is true and I was building a box for a 3" driver and I wanted my box to be 3" in depth the box size should be 3"x10"x13" ? Is this correct? or 4" in depth it would be 4"x10"x14"? It seems to easy as if I am doing it wrong.

I am looking for the smallest box possible without compromising sound response for the Tang Band W3-881S. I really need help! I am very new and don't understand the box dimensions. Please Help! I tried the freeware but that really does not help. I just need to know the internal cubic inches needed for one.

Jered22
 
http://mathworld.wolfram.com/GoldenRectangle.html

The math can look a bit daunting, but if you note the parts about what Euclid did with geometry, you'll get a pretty good feel for it.

As others have said, make the length of a rectangle equal to 1.61 times it's side and you're on your way.

Dig up a copy of "The Power of Limits" by Gyorgy Doczi for a good time. It starts with the appearance of the divine ratio in nature and art, and goes outward from there.

How come math was never this fun / useful / interesting in school?
 
purplepeople said:
Wouldn't it be better to use prime numbers for ratios?

:)ensen.

Actually, not really. The idea behind the golden ratio is that it's irrational; it's not a proper fraction. The actual number is 1.61803... the formula to find it is (1+sqrrt(5))/2.

As far as why it's been thought of as a good idea to use in audio, I think that's because you might have a 500hz standing wave between two panels, but with that ratio you will not have a standing wave at 250 or 1000 hz between two other panels.

If your box is small enough that the smallest wavelength in its passband is greater than 4 times the longest internal dimension (say, corner to corner), you shouldn't have any trouble with internal standing waves. Another way to fight internal standing waves is to use trapezoids, so the walls aren't parallel. This prevents large flat areas from being of a constant equal distance.

Here's a site with more information about the golden ratio, but I think they over-hype it just a little bit.

http://goldennumber.net/

Other ways to fight standing waves include fibrous stuffing material (poly-fill from wal-mart) in a regular tapered box, or in a tapered terminated tube- like the B&W nautalus.

So, I think that's why (other than looks) that you hear about the golden ratio in speakers. If anyone has more info, I'd be eager to hear it :)
 

GM

Member
Joined 2003
So if this is true and I was building a box for a 3" driver and I wanted my box to be 3" in depth the box size should be 3"x10"x13" ? Is this correct? or 4" in depth it would be 4"x10"x14"? It seems to easy as if I am doing it wrong.
How can it be? Using 4" as the base: 4/0.618 = ~6.47" and ~6.47*1.618 = ~10.47", but you have to find the proper volume (Vb) required for whatever frequency response (FR) you want (alignment). If not, then you will have to figure out its dimensions using either a golden or acoustic ratio (there's a bunch of acceptable ones). Or do like most folks and make them whatever dims you want and use as much stuffing as required to make it sound good to you. ;)
The big question is If I am going to be putting two Tang Band W3-881S into one enclosure what size does the inside measurments need to be for each speaker? If possible I would like to keep the depth around 4" and the enclosure taller than wider.
Well, I assume you will be using a sub and will be setting these speakers to 'small', but even then they won't play very loud without audibly distorting. Anyway, assuming the 4" is o.d., making the inside dim 2.5" assuming 0.75" thick material, then using one of the other parts of the golden ratio, 2.5*1.618 = ~4.03", and since 0.67ft^3 is required (Vb) the long dim = (0.67*1728")/(2.5"*4.03") = 114.91", probably somewhat slimmer than you had in mind and definitely not a good idea due to the strong standing waves well above/beyond the ideal for this driver if a ML-TL. ;)

So about all you can do if one dim is 2.5" is to multiply the longest internal dim you can tolerate by 2.5 (or other dim) and divide it into the Vb to find the width. Again, assuming a 0.75" thick baffle, the vent would be a 2" diameter hole. Add stuffing to 'taste'.

GM
 

GM

Member
Joined 2003
So, I think that's why (other than looks) that you hear about the golden ratio in speakers. If anyone has more info, I'd be eager to hear it
No, this is pretty much it. With the exception of MJK's and a few other programs, they all assume the cab has a ~uniform particle density so the only way the cab will perform exactly as modeled is if it is a golden or acoustic ratio with the vent exiting the bottom and the driver positioned based on its acoustic resonant center. If you ignore the vent's impact on this, then it will always be near/at the cab's horizontal centerline.

GM
 
markp said:
Actually, there are many 'golden ratios'. The idea behind them is that the product of all the dimensions is equal to 1. Notice that .6x1x1.6=1 and .8x1x1.25=1 and so on.


Yes, but Phi is not 1.6 exactly - it's irrational, (the 'most' irrational number in fact, beacuse it expands into more fractions ) and so it cannot feature in a set that sums to one.

(Unless, does the irrationality of the 1/Phi side of a golden rhombus negate the irrationality of Phi side? dunno.)

Either way, my mitre saw doesn't have a detent for the square root of 2, so the infinite series part of the measurement gets rounded off in the kerf. My point is theoretical, not practical.

In my understanding, the use of the term 'golden' denotes the presence of the ratio Phi (1.619...) so while the "golden ratio" may sum to 1, and other ratios may sum to 1, the golden designation is not conferred upon the others..

I am not a mathemetician, so I'm likely wrong... if I am, please explain more.

--humbly, Andy
 
There's a book out called "The Golden Ration: The story of PHI, the world's most astonishing number". (1/137's pretty good, too, but I digress.) Y'all might like it.

(The ratio can be found in all manner of living things, just by virtue of the way they grow... the nautilus shell is probably the most famous version... see Cardas.)
 
AndyN said:



Yes, but Phi is not 1.6 exactly - it's irrational, (the 'most' irrational number in fact, beacuse it expands into more fractions ) and so it cannot feature in a set that sums to one.

(Unless, does the irrationality of the 1/Phi side of a golden rhombus negate the irrationality of Phi side? dunno.)

Either way, my mitre saw doesn't have a detent for the square root of 2, so the infinite series part of the measurement gets rounded off in the kerf. My point is theoretical, not practical.

In my understanding, the use of the term 'golden' denotes the presence of the ratio Phi (1.619...) so while the "golden ratio" may sum to 1, and other ratios may sum to 1, the golden designation is not conferred upon the others..

I am not a mathemetician, so I'm likely wrong... if I am, please explain more.

--humbly, Andy
I am speaking practically not theoretically. Also take a look at the Fibonacci series for another explaination.
 
Or........
 

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Oh so stinky bad. Translational mode analysis of a prismatic space (rectangles) provides the most spreading of resonances with a ratio of 1.1.414x1.732. Square root of 1x2x3. There has been a lot of nonsense published about this considering some single aspect which misses the translational modes and only considers the main modes. But then wrong is always the most popular.
 
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