SLAT TYPE HELMHOLTZ RESONATOR FORMULA

Eric_Desart · Post by **Eric_Desart** » Wed Feb 18, 2004 10:37 am

Recently a very attentive person noticed an error related to published Slat type Helmholtz resonator formulas and reported this.

From: Scott Smith
Newsgroups: alt.sci.physics.acoustics
Date: 2004-02-02 15:45:49 PST

The noticed error was further investigated by the author versus diverse editions of the referred books.

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WRONG often published and in calculators used formula
fo = 2160*sqrt(r/((d*1.2*D)+(r+w)))

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CORRECT formula
fo = 2160*sqrt(r/((d*1.2*D)*(r+w)))

r = slot width
d = slat thickness
1.2 = mouth correction
D = cavity depth,
w = slat width
2160 = c/(2*PI) but rounded
c = speed of sound in inch/sec.

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DETAILS

There was some confusion about the origin of this error:
Both:
Master Handbook of Acoustics
Handbook for Sound Engineers
were referred as possible sources.

I took liberty to check different editions of the books themselves
Master Handbook of Acoustics - F. Alton Everest - editions 2, 3 and 4
Handbook for Sound Engineers - Glen M. Ballou - editions 2 and 3

The formula with the included error is:
2160*sqrt(r/((d*D)+(r+w)))

This error does NOT originate from "Master Handbook of Acoustics" but from "Handbook for Sound Engineers"

The correct formula is:
2160*sqrt(r/((d*D)*(r+w))) [+ sign to be substituted by *]
Both Handbook for Sound Engineers: editions 2 and 3 still show the faulty version.

Scott Smith reported his RIGHTFUL CONCERN about the spreadsheets he found on the net and reported at least 3 of them based on the wrong formula.

I took the liberty to check any further and came to the conclusion that for "Slat type Helmholtz resonators" I could not come up with even 1 single correct calculator, neither HTML, nor Java or Excel calculators.
So this problem seems even worse then reported by Scott Smith.
The faulty "Slat type Helmholtz resonator" calculators on the net are NOT the exception but the rule!!!

Even the calculators on highly respected sites as SAE:

http://www.saecollege.de/reference_mate ... mholtz.xls http://www.saecollege.de/reference_mate ... encies.htm
but also others as e.g.:

http://homepages.tig.com.au/~audio/elec ... lmholz.htm
http://www.mhsoft.nl/Helmholtzabsorber.asp
http://www.mindspring.com/~c_campbell_2 ... mholtz.xls
are wrong.

This error does not appear in the "Master Handbook of Acoustics - F. Alton Everest"
So why are that many calculators wrong, knowing That F. Alton Everest is also a standard work in the studio world?

Lets analyse both approaches:

1) Handbook for Sound Engineers - Glen M. Ballou - editions 2 and 3

fo = 2160*sqrt(r/((d*D)+(r+w))) (note this is still the Wrong formula)

d = the effective depth of the slot in inches, which is approximately (1.2) x (thickness of the slot in inches)
Important to note is that the factor 1.2 is an approximation.
The correct mathematical modelling of the mouth correction for Slat type Helmholtz resonators is a rather complex business.

2) Master Handbook of Acoustics - F. Alton Everest - editions 2, 3 and 4

fo = 216*sqrt(p/(d*D))

fo = resonance freq.. in Hz
p = perforation percentage (noted as values 1 to 100%)
D= airspace depth in inches
d = thickness of slat

p = 100 * r/(w+r)
r = slot width
w = slat width

One notices that F. Alton Everest ignores this (in reality complex) mouth correction.
It is not that uncommon that lots of books, even respected works only present stylized versions of formulas.
Any work is written in function of a specific target group.

As such works as the "The Master Handbook of Acoustics" will go less deep in mathematics as more specialized works.

While the aforementioned noted factor 1.2 for the mouth correction in the "Handbook for Sound Engineers" is only an approximation, it's still better to use this approximation than ignoring the mouth correction.

What is this mouth correction?
A Helmholtz resonator is a mass-spring system, which is comparable with a panel or membrane resonator.
The system is based on a mass which vibrates in resonance on a spring.
The ratio of the mass versus the dynamic stiffness of this spring defines the resonance frequency.
The air layer in the cavity acts as a spring with a certain dynamic stiffness mainly defined by its volume.
The larger the Volume, the weaker the spring becomes (lowering resonance frequency) and vice versa.

For a panel resonator it's easy to imagine what the mass is: the panel.
The heavier this mass becomes the lower the resonance frequency and vice versa.
As such a panel resonator is mainly defined by the combination of both properties.
This isn't complete, since angle of incidence, weakness of spring, damping etc. will influence the resonance frequency and the Q-factor.

For a Helmholtz resonator this mass is represented by the mass of the air enclosed by the neck or slot of the resonator.
However this apparent mass extends outside the exact geometrical boundaries of this neck or slot.
This is covered by the mouth correction, which is in fact a correction factor increasing those geometrical boundaries.
In reality this phenomenon is much more complicated than the simple factor, used by the traditional formulas.
As such the distance between those necks or slots (interaction) and others will influence this correction.
For practical use however the standard formulas are a good approach.

I can only assume that it is the lack of this mouth correction in Everest's formulas why Ballou's formula (but correctly printed in Michael Rettinger's book on Studio Acoustics) is used.

In fact one can call it incredible that so many calculators on the net are wrong, even from well respected organizations as SAE, which is and presents itself as:
"The largest Institute for Multimedia, Audio Education and Digital Film Education worldwide"

NONE of the calculators I found mention the source of the used calculation method.

And here Some EXTREMELY important comments, in relation to the error reporting by Scott Smith, are due

From: Tony Woolf
Newsgroups: alt.sci.physics.acoustics
Date: 2004-02-04 10:46:33 PST

...I found your post a useful reminder that published equations can have errors.
For this reason and others, it is dangerous to pick up and use equations that you are not familiar with and do not understand.
Your post also made me realize that is not nearly so easy to see an error in an equation in spreadsheet format as it is in conventional notation, and I think this is also worth remembering ...

From: Noral Stewart
Newsgroups: alt.sci.physics.acoustics
Date: 2004-02-04 17:56:50 PST
<SNIP>
.........that many of us in this newsgroup know that errors exist in even the most respected works and we watch out for them.
However, those in some other newsgroups might be more inclined to take anything in print as gospel and spread it.
I can point out errors in almost every book I have. For some, I even have lists for various editions.
Errors are there for a variety of reasons.
<SNIP>
Unfortunately, we are plagued by many people who trust equations and and data they find without verifying them or without asking the conditions that make the data valid.
These same people buy computer programs with limitations and possibly errors they do not understand, and suddenly think they are an expert.

Note from the author:
It is indeed incredible, and this is certainly valid for the studio world, how many data is copied from site to site, without any respect for the author or source of the information or used calculation methods.
Is this done just to look clever? To attract people to there site? To present themselves as experts?

The above example is a SCHOOL EXAMPLE of this type of behavior.
It most likely started with nothing more than a simple typesetting error remaining unnoticed.

As it seems now, the resulting WRONG calculation formula used by so many sites became the standard rather than the exception.

Why then did educated acousticians didn't noticed this before?
Mostly professional acousticians do NOT rely on net calculators, but on there study and books.
And here the comments by Noral Stewart are important.

For a trained acoustician a formula is a mathematical representation of a physical process.
As such it is a language in the same manner the written word is the tool for a writer to express his thoughts.

Anyhow the author wishes to express his respect to Scott Smitt for:
a) Reporting this.
b) Being critical enough to notice this error.

Further the author expresses his respect:
1) Tony Woolf (Europe: UK acoustician - http://www.tonywoolf.co.uk )
2) Noral Stewart (US: NC acoustician - http://www.stewartacousticalconsultants.com )
For their valuable comments

3) J.F. Oros (member http://forum.studiotips.com )
4) Jack Hildwine (member http://forum.studiotips.com )
5) Jeff D. Szymanski (Chief Acoustician: http://www.auralex.com )
For checking the exact content of the by the author lacking editions of Everest's and Ballou's books.

Eric Desart
http://www.acoustics-noise.com

Post by **John Sayers** » Wed Feb 18, 2004 8:59 pm

Wow - that's interesting Eric and embarrassing

Mate I think I probably got my formula from the "Handbook for Sound Engineers" as it was a standard textbook at the University where I taught sound engineering. I'm afraid I trusted it.

I first used the formula in my "How to Build a Recording Studio" site which I posted back in 97/98. It then became "The Recording Manual" that was eventually sold to the SAE in 2000 who have since offered it in their reference material section.

Naturally I accept full responsibility for misleading people by using an incorrect formula and to everyone I apologise.

It's interesting because the difference in the Helmholtz formulas came up a while back on your Yahoo Acoustics Group where someone questioned the different results given by different formulas on the web. I do remember you pointing out then that some of the calculators were incorrect and you did post the SAE one as being a correct one.

cheers
john

knightfly · Post by **knightfly** » Wed Feb 18, 2004 9:38 pm

Eric, thank you VERY much for including us in the loop - I'll be modifying a spreadsheet or two when I get some time.

(Just what I need, another project

)

Thanks again... Steve

Eric_Desart · Post by **Eric_Desart** » Wed Feb 18, 2004 10:30 pm

John Sayers wrote:Wow - that's interesting Eric and embarrassing
It's interesting because the difference in the Helmholtz formulas came up a while back on your Yahoo Acoustics Group where someone questioned the different results given by different formulas on the web. I do remember you pointing out then that some of the calculators were incorrect and you did post the SAE one as being a correct one.
cheers
john

Hi John,

I can't remember, but it's very possible.
I must say I never checked them, and I don't use Net calculators.
I'm maybe 3 year on the net, and do acoustics >> 25 years.
And indeed I always automatically trusted SAE as a safe site to refer to.
So if I did I'm guilty too,

(lucky you left one blush).

And for whatever reason: slat type Helmholtz resonators relative seldom came up there (I wonder if I'm looking for an alibi

)

Anyhow when this Scott pointed this out I started investigating.
He originally thought it was Everest, so I think he also found those references via, via...
So I don't take credit for some very clever guy with some healty critisisme.

Cheers
Eric

PS: If you wonder what I used/use:
Being Dutch my Univ books are Dutch courses made over the years by the Univ/Profs itself.

But a very good book which goes much more in-depth:

BAUPHYSIKALISCHE ENTWURFSLEHRE
BAU- UND RAUMAKUSTIK
by FASOLD, SONNTAG, WINKLER
Publisher: Rudolf Müller - Berlin 1987
ISBN 3-481-12421-X

Problem this is East German.
With the unification of Germany this Publisher disappeared.

If you or anybody else should ever find this book back (I still have an overused copy) I'm certainly interested.
Believe it or not, but books from the former communistic countries were often extremely good.
Reason (as a Prof told me): They invested enormous amounts in knowledge and the profs themselves had little personal gain (very low salaries). They published all they knew.

Eric_Desart · Post by **Eric_Desart** » Wed Feb 18, 2004 11:10 pm

Hello Steve,

I won't forget you héééééééé!!

Just fun:

1) If a studio guy accidentally comes here first than his studio is dominated by slat type Helmholz resonators.
2) If He came 3/4 year back at RO then his studio was a collection of paneltraps.
3) Now a fresh guy at RO makes it cornertraps or MiniTraps.
4) A visiter at Yahoo by definition ended up with corner traps.

So what's good: I'm not home anymore

:?:

knightfly · Post by **knightfly** » Fri Feb 20, 2004 1:39 pm

You forgot - My personal favorite
(5) The Trap that puts the Snap in your mix - special pricing for Mickey Mouse Club members. (the trap can be converted to broadband by simply using a small swatch of 703 placed on the yellow platform...

knightfly · Post by **knightfly** » Fri Feb 20, 2004 2:03 pm

BTW, just changed the SAE calculator formula, and with the same 5/100/400/25 values, the old one returns center freq of 201 hZ vs 109 hZ for the correct formula. Another set of values puts the difference at OVER an OCTAVE - Oops... Steve

cadesignr · Post by **cadesignr** » Fri Feb 20, 2004 11:07 pm

Hello gentleman, not being mathimatically enlightend, this is out of my league, but it would seem, IF these were designed to absorb a specific frequency, like a room mode, and they did NOT work as calculated, why hasn't anyone heard it after all this time. Seems kind of......unnoticed? Or am I not understanding the design purpose. I always thought that things that did NOT work would be noticed right away? Especially if a room was tested? Or is this so vauge that the ear cannot distinquish if it is working or not? I mean, whats the point of a VERY specific formula, if no one can even tell if it is doing what it is designed to do? Please do not take this as anything but curiosity.

fitZ

bassman · Post by **bassman** » Sat Feb 21, 2004 1:27 am

One thing I wanted to add to this is that making panels, or in my case gobos, with varying gaps between the slats does not yeild a more wideband absorber by having multiple resonant frequencies. My understanding is that the average gap dimension becomes the resonant frequency variable. Looks nice but doesn't give you different frequency absorbtion unless the cavity beneath each variance in gap is separated from adjacent cavities with other gap sizes.

Those hemoltz traps can be tough.

-bassman

knightfly · Post by **knightfly** » Sat Feb 21, 2004 2:29 am

"doesn't give you different frequency absorbtion unless the cavity beneath each variance in gap is separated from adjacent cavities with other gap sizes" -

Yeah, Barefoot mentioned this quite a few months ago - has to do with the wavelength being much larger than the trap in most cases, so the AVERAGE pressure across the trap tends to dominate rather than each slot being autonomous. (Unless, as you said, you place individual septums between slot cavities, in which case you have several small independent Helmholz traps, any one of which wouldn't have a lot of effect) but taken together, if the face were slanted creating a different depth (or different slot width/slat width, or all of these), then you would effectively create a more broadband trap.

Rick, one possible reason few people have noticed is that the change seems (so far, with limited tests) to produce close to an octave difference. Can you say "harmonic" ? I'm thinking that the end results would have been close enough to an octave that the traps would still help in most cases. So far, not that many people actually use room analyzers/software and "shoot the room" - more often, they just listen to "golden" CD's and say, yeah that works...

That's just a theory of course - I'm still looking at this, as I'm sure a LOT of people are... Steve

cadesignr · Post by **cadesignr** » Sat Feb 21, 2004 3:27 am

Hello Steve, thanks buddy, here is another one for ya

Alright, lets imagine, you've done all the analysis of a room, but before you do ANYTHING to a bare bones room,(control room) you install nothing but your speakers, an amp, and a playback device or signal generator. Assuming the room is soundproofed enough, and the interior shell is built as part of the absorbtion calculation criteria etc, would it be safe to assume, that if you energized the room with a signal gererator from 20 hz on up, this would tell your ears exactly what the room was doing with NO treatment. After all, isn't this what all this is about. Anyway, wouldn't you HEAR resonance or, room modes, at various frequencys from the generator, and with a digital one, it should tell you exactly what those frequencys are?
And if this is true so far, IF you were to bring calculated treatment (slat tresonators etc) into the room and run these same frequencys, it seems reasonable to me, that either you would be able to tell whether they are working or not, simply by placing a sheet of ply or something over the slots, and removing it. Would not that cause you to hear the resonance when the cover is removed? I know this sounds simplistic, and it is, cause damit, either you can hear this stuff working or NOT working, right. Or, to my way of thinking, if not, what is this, the emporoers new clothing

Just kidding, but in a way I'm not as I am really curious now exactly what it is your SUPPOSED to hear if they indeed are working.

fitZ still

knightfly · Post by **knightfly** » Sat Feb 21, 2004 5:23 am

Sorry Rick, gettin' too close to draggin my sorry ass to bed for one of these - prob'ly tomorrow night (BTW, it's NOT quite that simple, since music isn't made of sine waves very often (flute solos possibly excepted)

Also, if you cover a helmholz with a solid sheet of plywood, you've just (sorta) created a panel trap

I'll get into this more soon... Steve

Eric_Desart · Post by **Eric_Desart** » Sat Feb 21, 2004 7:21 am

Hi all,

I see a lot of rightfull questions here.

I have no time to go in-depth. This is not to hide something, but because lots of it can't very simply be answered, and lots I just don't know exactly.

Your soundfield that you generate depends for the traveling waves on the combination direct field and boundary interference. So directionality speakers and sound propagation come into play.

For the standing waves (room modes) directionality doesn't come into the picture (at least not in function of source radiation), but the position of the source will be defining for the strenght of the excitation of the diffent modes.
Axial modes behave as plain waves straight to the walls.
Tangential modes as wave fronts in relation the the diagonals (depends on order) in 2-D plains, but form a rather complex pattern for higher order modes.
Oblique modes as wave fronts in relation to the diagonals in a 3-D space, but form a rather complex pattern for higher order modes.

Slat type and other Helmholtz resonators are angle of incidence dependent, but are also influenced by other factors.

I'm saying this all to make clear that exact tests to check formulas calls for a lot of boundary conditions, one must either understand, or measure in measurement rooms where the field is better known.

Note that all those resonator formulas assume a lot of boundary conditions and are based on simple conditions, and that for exact tuning one better checks that in practice.

Those Helmholtz formulas as well as Panel trap formulas are nothing else than the room acoustic translation of a simple 1 DOF mass-spring system.
This means in analogy : a small mass, as a piece of wood, on a helical (or other linear) spring on top of a table.

I think I have a little bit different vision than Thomas on those things.
I see Thomas using a lot of wavelenght relations (which of course is partly involved).

The way slat type Helmholtz resonators are used here are rather broadbanded. Also the different slat widths, while certainly usefull are difficult theoretical to define. The law of inertia certainly plays a role in the cavity. The stiffness of the spring will try to smooth out, while simultaniously one gets in fact a higher order mass-spring system (multi- DOF = Degrees Of Freedom).

What I'm saying is: be careful with explenations, just because it's easy to have one.
I think a lot of systematic testing is needed to isolate some of those phenomena. Without having access to such data (published or measured) it's very risky to see certain explenations as facts.

One of the risky things that I notice on the net is:
Someone tries to figure out why something happens or just is: He suggests some possible well thought through options. For one or the other reason, while never tested, and by the originator only suggested as still to be investigated thoughts, they become fact on the net.
Just because it's easy to give things a name or simple definition.

Too many well meant assumptions from searching minds became facts.
And checking formulas and measuring resonance frequencies based on real life circumstances is very good and even advisable for specific applications and use, but risky if used as a generalization of the phenomenon without controlling and understanding all boundary conditions.

Eric

Here I have also a question for Thomas:
Thomas I heard you say at RO that the efficiency of a helmholtz or slat type Helmholtz can be somehow related to the ratio of open (slots) to the closed (area).
Have you measurements or publications confirming that?
E.g. A single 10 ounce Cola bottle at river banks resulted in 5.9 sabins.

I can't find that back, nor do the measurements I know confirm that (certainly not as some kind of linear relation).
I admit I never investigated that, but still have lots of data in which I can't recognize this. And I have books that remain very vague about it, while going very deep where mathematical approaches can be used.
And the afforementioned Cola bottle gives rather impressive results.

What I once tested was an extensive series of perforated thin steelsheets on top of rockwool (300 mm and 100 mm thick; surface ca 12 m2).
This test was done in function of investigating the acoustic transparency of those thin steel sheets for industrial purposes.

I tested between ca 4.5 % to 70 % perforation.
Also there nothing related systematically to this ratio.
In fact what we mainly found was a (still further to be investigated, since no main perpose of study) relation between the closed surface measures and the wavelenght in function of reflection/scattering.
Note: all those test were performed by myself in an official Univ reverb lab as per ISO 354 standard (standard absorption measurements).

Kind regards to all
Eric

PS: A question to Steve or other mods.
I write an enormous amount of spelling errors, maybe wrong words.
This is all very time consuming for me.
If usefull, please edit my messages to correct such things but as well please without altering the content.

knightfly · Post by **knightfly** » Sat Feb 21, 2004 5:41 pm

Rick, one of the problems with your approach (not that it isn't possible) is human persistence - if you do AB testing between any two choices, the time lag between tests needs to be at or near zero or our mind forgets exactly what the other one sounded like. This is partly why test software can be helpful, if you know enough about acoustics in the first place NOT to let the software lie to you by doing wrong tests, or in the wrong way, wrong place, ad nauseum...

Still, that's pretty much what I intend when I get to that point - set up what you KNOW will be necessary, fire it up and listen. Between "golden" CD's and high res plots of each speaker in position separately, then in combination, etc, one should be able to figure out from the combination of listening to music and comparing graphs, just what kind (and generally how much) of treatment is still needed to reach the goal for that room.

Eric, the way the board is set up I only have editing capability for posts in the Construction forum - plus, I don't think I should put words in other peoples mouths, although if you're asking, I might clear up syntax a bit and notate at the bottom so you can check it - Either your english is improving or my interpretation is getting better, because I understand a LOT more of your posts than I used to - I really wouldn't worry about it if I were you.

I'm posting the corrected Helmholz calculator as a sticky here (or if that doesn't work I'll do it on the Construction forum) - I kept the old formula as well, and labeled it for comparison so it's really quick to see what the old and the correct formula results are... Steve

cadesignr · Post by **cadesignr** » Mon Feb 23, 2004 2:42 am

Too many well meant assumptions from searching minds became facts. k

Give me a break Eric. Sounds like the shoe is on the other foot to me. Your the professionals. And yet this formula has skipped by for how many years. Talk about fact. How bout diffusion in a small room. I bought that one for years, because Everest ballyhooed it in his book. Now every website I read about diffusion says it theres no such thing as a diffuse sound field in a small room. He even shows pictures of diffusers in SMALL ROOMS and describes the effects on music listening, AND gives graphic representation. So who is the ones passing info as fact, if indeed its not the professionals. Maybe YOU can explain why after all these years no one has come forward complaining why thier hemholtz resonators arn't working as you should be able to HEAR it. Or is this some kind of no hear, no know if its working deal. I mean, what the hell are these for if not to remove offensive AUDIBLE frequencys? Layman maybe responsible for the use of technical issues in incorrect ways, but they seldom are responsible for PUBLISHING professional journals and documents with error and so called facts that are later tossed to the wind like so much acoustical brain farts. And frankly, spending $25 on this book makes me pissed as I spent many hours trying to decipher the elements of diffusion from a laymans point of perspective for my SMALL ROOM!. Only to be told years later it doesn't work in small rooms. So I say it again, give me a break. What you professionals seem to forget is your TRUTH is the very reason layman come to these bbs's as I doubt if any interested layman with half a brain would waste their time on net fact crap. How bout this. The use of 703 has spread across this planet in less time than an outbreak of SARS. And why? Only because the word of professional studio designers and acoustitions. But now, my trust in professional acoustical word has been betrayed. Whats next, the speed of sound is an error? Besides, I'm tired of elitist ivory tower suppositions of superior thinking vs layman capabilitys. Millions of records have been made in less than perfect acoustical conditions, and some of them have terrible acoustics, but I don't give a damn, as I, like most mortals, llisten to the music. NOT the acoustics.

fitZ