The "Golden" Ratio?
I try to consider every aspect of loudspeaker design when I make one. Before I make anything, the ratio of dimensions has to be determined. Now, I understand some (most?) people don't care about the "golden ratio," but the most baffling fact is that I've found several ratios out there that claim to be "golden." On the Index of Resources section on their website, Parts Express says that it is 2.6/1/1.6 (h/w/d). But according to an old Radio Shack book, it's 1.6/1/0.6 (h/w/d). They do look different, don't they?
I generally want the depth of my enclosures to be considerably larger than the width, so I trust PE more. (After all, who's to believe the Shack?) However, PE's ratio seems to apply only to dual-woofer or MTM designs (the Joe D'Appolito configuration). I mean, for a two-way with a tiny midbass, following that ratio means you can't even fit the darn midbass on the front!!! Surely no tower or floorstander follows that convention. And with the advent of plasma, some HT speakers are now designed to complement them. (The ratio doesn't matter as long as it's not deep!)
So, for the time being, I'm using average dimension ratios from "normal" commercial systems as a starting point. (Count out the B brand!) I'm really looking for a good ratio suitable for a small two-driver two-way.
They are the same with the width and depth interchanged,
i.e. "2.6 to 1 to 1.6" is the same as "1.6 to 0.6 to 1".
If you dont like this shape then you play around by halving one ratio :
giving h=1.6, w=1, d=1.3, suitable for a two way.
This is about the golden ratio only, I know next to nothing about
The golden ratio is just a numeric constant, but an irrational one
so it can't be written down exactly. Hence, it is usually
approximated by a rational number, that is as a ratio between
two numbers. 2/3 is a crude approximation, 3/5 a sligthly better
one, 5/8 yet a better on. In fact, you can get arbitrarily close to
the golden ratio by taking the ratio of subsequent pairs of
numbers in the Fibanacci number series which starts as
and where each number is the sum of the two preceeding ones
in the series. You see from this series where the approximations
I gave above come from. The golden ratio has a strange tendency
to pop up in various situations as diverse as art, optimizing
certain data structures for computer programs and, obviously,
loudspeaker design. BTW, Fibonacci invented his number series
in an attempt to find a mathematical model for how quickly
Back to the speakers then. I don't really know, but I suppose
what you want is a box dimension AxBxC s.t. B/A is the golden
ratio and C/B is the golden ratio. So in the case of 1.6/1/0.6
you referred to we have 1/1.6 = 5/8 which is a "standard"
approximation of the golden ratio, and we have 0.6/1= 3/5,
which is also a standard approsimation, but a cruder one. If
you really want golden ratios, you should probably adjust
at least one of these ratios so they have the same "degree"
of approximation, ie. both being 5/8 for instance. While the
increasingly refined approximations given by the Fibonacci
series give increasinly lower error, they do have a tendency to
alternate between positive and negative error. Hence, if you
use different ratios for the approximations of the box dimensions
you increase the error unnecessarily. Then what
precision you need, or if golden ratios are even good for speaker
design, that you have to ask somebody else.
Anything beyond 2 decimal points of accuracy tends to be swamped by other issues in the construction of the loudspeaker.
It is best to use that minimum of two decimal points in the design/measurements/cutting of the design, otherwise errors do increase.
According to the radio shack book i have you can use either
.6 : 1 : 1.6
.79 : 1 : 1.25
Thanks for the interesting info here, everyone. Maybe I'll have to look into devising my own ratio for each type of speaker (i.e. mini monitor, dual-woofer, etc.). About that Radio Shack book, sardonx, I probably have the older edition...
If I can pick your brain a bit more, the reason for the use of golden ratio's in speaker dimensions is that it would avoid standing waves appearing of the same wavelength or multiples of it in more than one dimension. Meaning that there should not be a standing wave in the width of say L, while at the same time there would be a standing wave of 2L in one of the other dimensions, L of course being determined by the fact that it would be an integral of the dimension.
Do you agree that this golden ratio in speaker dimensions is a good one to avoid these multiple-wavelength standing waves? Could there be a better one?
I like your clarification of the golden rule with the link to Fibonacci. This is based on the simple mathematical equation b:a = (b+a):b. Some fiddling around with this equation shows that b:a = 2/(sqrt(5)-1) which is 1.6180339887498948482045868343656.
This requires an highly accurate sawing-machine and skills. ;)
The ratios are much more applicable to room modes in acoustics.
In speakers you can damp the internal modes into insignificance.
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