The "Golden" Ratio?

[Christer]

Originally posted by janneman
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?

Yes, I thought that was the reason. Or rather, I suppose we
want to find a relationship s.t. for each pair a,b of the three sides
of the box, we never have the case that both a and b are both a
multiple of the wavelength for any frequency in the audio band.
Or maybe multiple of half the wavelength is more appropriate?
It's been very long since I took the course on wave propagation.

I don't know if the golden ratio is guaranteed to achieve this
and if so if it is the only number achieveing it. If it does not
guarantee this condition, then maybe it is still the best choice
or maybe it isn't really known if that is the case. I am not a
mathematician so I have no clever answer here. However, I
wouldn't be the least surprised if it has been proven that the
golden ratio is the optimal value. That number as well as the
Fibonacci series has an almost magical tendency to appear even
where you least expect it.

Then, let's not forget that this is only the theory and since
element positions must be taken into account,
elements are not mathematical points etc. the best practical
values may very well be off from the theoretical best ones.

Originally posted by Steven
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.

You ought to get yourself a better sawing-machine, then you may
use this approximation instead
http://www.cs.arizona.edu/icon/oddsends/phi.htm



Edit: As i said, the golden ratio has a tendency to show up
where you least expect it
http://www.golden-ratio.co.uk/

[sreten]

Originally posted by janneman

I'm not so sure about that. Are you talking about filling the internal space with damping material like sheeps wool etc?
Jan Didden

Well I'm pretty sure. If you can't measure it its not there. Acoustic
damping in speakers is very effective at the wavelengths that are
relevant. Its only an issue with minimal internal acoustic damping.

sreten.

[Vikash]

I suggest reading this thread

You may also find this useful to calculate enclosure/room modes.

[GM]

>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.

====

Right, while the golden ratio collapses at the 8th harmonic, this one makes it to the 10th.

====

>According to the radio shack book i have you can use either

.6 : 1 : 1.6

or

.79 : 1 : 1.25

====

There's actually numerous acceptable acoustic ratios, some better than the golden ratio, but in most cases, any ratio that works out to the 4th or 5th harmonic is sufficient.

The asthetically pleasing 1:1.4:2 often seen in architecture is good to the 11th harmonic, and 1:1.26:1.41, 1:1.17:1.47, and 1:1.45:2.10 are (were?) popular speaker cab ratios.

If you can find a copy of Bolt, Beranek, and Newman's acceptable room ratio graph you can choose many more, or just plug whatever numbers you want to use in a room mode calculator to see how well they work.

====

>The ratios are much more applicable to room modes in acoustics.

In speakers you can damp the internal modes into insignificance.

====

I agree it's moot WRT the typical small two way monitors currently in vogue, but this often requires too much stuffing IMO if 'fullrange' drivers are used and/or the cab is fairly large.

GM

[uvodee]

Originally posted by Christer
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
rabbits multiply.

You are so right, my friend, and that the television industry is not following this rule by 'inventing 16/9 format explains immediately why lookin nowadays tv screens give you unnatural looks, and actually tires you out when trying to see the picture.

Jean-Pierre

[coolkhoa]

I've realized that most small speakers ignore the golden ratio altogether (either for aesthetics or because of the fact that using such a ratio means the driver(s) cannot fit on the front panel). In fact, I've seen small speakers that are square or are nearly square in two dimensions (usually width and depth).

My question is: does an enclosure with a dimension 1.5 times larger than another just as bad?

[Vikash]

does an enclosure with a dimension 1.5 times larger than another just as bad?

Just as bad as what? Any dimension which is a the same as another will have the same standing wave fundamental and harmonics. A dimension which is easily divisble by another dimension will have some clashing standing wave harmormics. So 1.5 times is not as bad as having two the same, but is bad nevertheless.

See how the 2nd and 3d, 4th and 6th harmonics clash for your 1.5 times example. But it's not nearly as bad as having two dimensions equal

I've realized that most small speakers ignore the golden ratio altogether

The smaller the dimension, the higher the standing wave frequencies. At 7cm for example, the standing wave fundamental is 2.4kHz. I think (though not sure) that for a reason related to the high frequency, small enclsosures do not have the same concern of standing waves (less enegry perhaps = more easily suppressed by stuffing/frequency handled by tweeter?)

[sardonx]

"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..."

I have Advanced Speaker Systems from radio shack.. and yeah i guess this might be newer than the one you have because i had one before this too... an older version (probably the one you have) but it got torn apart from laying around the floor too long.. lol. This book teaches lots of stuff.. nothing too in-depth but a useful book to have.

[planet10]

The Golden Ratio is just an especially pleasing irrational number... irrational numbers are your friends.

dave

[markp]

Originally posted by planet10
The Golden Ratio is just an especially pleasing irrational number... irrational numbers are your friends.

dave

But irrational people are not!