SLAT TYPE HELMHOLTZ RESONATOR FORMULA

[Eric_Desart]

Hello Fitz,

"...Give me a break Eric...."

Sorry Fitz, how can you make this personal?
I even don't know you.

If it sounded like that, then I'm really sorry.

I started this thread, to report an error, and to explain some background.
I wanted to show the limits of even CORRECT formulas and the fact that they are valid within certain boundary conditions, by explaining what the physical origin is of those formulas (the mechanical mass-spring 1 DOF system).
You were searching, wondering. I DO LIKE searching/wondering people.
If well meant there are NO stupid questions. I'll have them too, and the more answers I get, the exponentially more questions I have. And that will be the case until I die.
Once I tell I know it all, it only means that I got crazy somehow, needing a medicin.

You blame professionals:
In this case it started with a typesetting error, which are possible in any book. If it happens in text, no problem, our mind reads over it.
It's annoying that it happens on such an important spot as interchanging an operator in a formula.
But in fact I answered your question already before.
E.g. I never in my live relied on a net calculator: Why? I studied physics from the basics, I have my own books and courses. If I see a Helmholtz or a panel trap formula then I know where it comes from, the basics behind it.

I'm also not used to see Imperial factors. So I lack feeling for such formulas before I converted them to metric. And mostly one must look to the source of the page to find the formula (if accessible) often difficult to read in Java or HTML language, since the symbolic notation of the formula is VERY SELDOM to be found on the page itself.
So a real expert, will not necessarily notice an error in a formula, just by seeing the calculated result. If the standard symbolic notation of the formula should be shown, then his build-in alarm should much easier be triggered.

Also Noral and Tony explained.

The biggest problem on the NET in the studio world are NOT the real acousticians, but the ones THINKING they are, or like to present themselves as the expert, and copying things from site to site without ever mentioning the source, just in order to look clever. And this alinia I DO MEAN with everything I stand for. The net is poisened with this kind of stuff.

So sorry for any possible misunderstanding.

Kind regards
Eric

[knightfly]

Rick, neither Eric nor I MADE the mistake in the helmholz formula, we're just trying to correct it. And neither of us INVENTED acoustics, we only STUDY the subject. I know you're trying to understand acoustics enough NOT to make any serious mistakes in building your recording space, as am I. I don't consider myself anywhere close to finished with acoustic study, only a lot further along than I used to be.

I get the impression from time to time that you think acoustics is a simple subject, with only one answer to each question - I'm sorry, but that's just NOT the case. If it were, then room modeling programs like CARA wouldn't take DAYS on a 3 gig pentium to model a room with just an average amount of detail input.

Don't think I don't understand your frustration in this - I've been trying to get a handle on the subject off and on since 1982, and it's only been in the last year or so that I've made any serious breakthroughs - and mistakes, no matter where they come from, don't help that.

It's late and I should be in bed, so I'm not gonna sugar coat this any more than you just did - your comment that you don't give a damn is bullshit. If it were true, then you wouldn't read, study, or post anything about the subject. Your comment about just listening to the music is also bull - most of the tonality of a mix usually comes from acoustics or the lack of them. Things like slap echo, flutter, uneven reverb, honky vocals, too much reverb, too dry, swishy flanging sound on cymbals, etc, ALL can be caused or eliminated with acoustics. Some may just be the fault of the recording engineer for not knowing enough about acoustics to pick the right spot in the room for the instrument or the mic, etc. Bottom line is, that's what the song sounds like. If it's different, or quirky, the song may gain a following BECAUSE of acoustics giving it that "different" sound. There are all kinds of different reasons why people like or dislike music, and that's one of them.

As far as I'm concerned, people like Eric and I, and a small handful of others, DONATE our time to try and help others understand a very complex subject so they can do things to improve their musical environment. As Eric pointed out, we are not Gods but students ourselves, and as such, if/when we learn new things we tend to share them - if the subject is too complex for you, either study more or leave it alone.

But do NOT come here and tear US a new asshole because we tried to HELP - shooting THIS particular messenger can be dangerous because I tend to shoot back. And once you've alienated the 8-10 people on the net who actually CAN think with your rants, who's gonna try to answer your questions - you know, the ones you dont give a damn about?

As you so aptly put it to Eric, gimme a BREAK... Steve

[AVare]

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.

Diffusers also reduce the amplitude of the peak reflections. You put diffusers in a small room on the back wall. This reduces the level of the refections and thus the comb filter effect. Better sound quality. No diffuse field, but better sound quality.

I spent many hours trying to decipher the elements of diffusion from a layman's point of perspective for my SMALL ROOM!. Only to be told years later it doesn't work in small rooms.

I have found in several different fields that at times I had problems understanding certain ideas because I did not quite understand the basics clearly until explained a different way. Perhaps my previous paragraph will help you in the same manner.

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.

Acoustics, especially control room acoustics, despite its massive amounts of objective study and analysis is still very much an art. When dealing with absorption, the interactions are not theoretically very predictable. Read the BBC RD report 1991-07 (its on their website) as an example of how even professionals do not have a predictable (Mathematica) model for real room acoustics with various types of absorption.

When designing a room we work with very specific numbers. In reality the one must understand th significance of the numbers. In the case of Helmholtz absorbers, the design criteria is the centre frequency, yet the effective bandwidth can be several octaves wide, depending the % open area. How often have you read about taking that into consideration? So the actual peak absorption frequency is off. The effective bandwidth could be so wide that the practical effect, especially if the following paragraph's procedure is not followed, is not noticed when listening.

Amateurs usually do not have the time or desire to:

test,
analyze,
guess at the causes of problems,
implement hopefully successful solutions,
and then repeat the process.

A second factor is that most rooms will be acoustically improved by the treatments regardless. This does mean that the room is at its potential best? No. But it is significantly improved.

I hope this helps understand the situation.

When I started to write this post I was going respond in the same style as your post, but after thinking about it, I felt that an informative response would help much more than an emotional rant.

Andre

[knightfly]

Andre, good comments and point well taken.

Normally, I would have been either more gentle or else gone to bed and answered when I was less irritable - however, in this case (since you're relatively new here) a bit of history - Rick and I consider ourselve friends, thru over a year of net interaction (and his recent move to within driving distance, even though we've not yet met) - he gets frustrated with this subject (as I've done), he vents, I explain a thing or two, tell him to "shut the f--- up, he calms down and continues his quest for knowledge. It's kind of a personality thing, he and I both understand it (I think) and we're still pals ( I hope) and, if he actually "goes away", I'll hunt him down like a dog and bash his head in with an acoustics book...


When we actually physically meet, I'm gonna kick his ass Gawd, will that be funny - two old farts wrestling around in the mud, both too stupid to realize nobody's winning... Steve

[Soundman2020]

This is a rather old thread, but I was just going over it again and I found an explanation by Erir Desart that I found to be very interesting, and worthwhile repeating, regarding the complexities of calculating with Helmholtz equations. At the end of his post, Eric said: "I write an enormous amount of spelling errors, maybe wrong words. This is all very time consuming for me. If useful, please edit my messages to correct such things but as well please without altering the content." So I took the liberty of doing exactly that, editing Eric's message, in order to try to clarify what I think Eric meant. From personal experience I know how hard it is to express complex thoughts in a foreign language, so I wanted to try to help out and make Eric's explanation a little more fluid, and easier to understand.

Eric, if you read this and don't like what I did to your text, then PLEASE tell me, and I'll happily delete it or correct it!

The original post is here: http://www.johnlsayers.com/phpBB2/viewt ... 996+#p9996

-- ERIC DESART PARAPHRASED --:

Hi all,

I see a lot of good questions here. I don’t have the time to analyze this in-depth. This isn’t because I’m trying to hide something, but rather because lots of it just cannot be answered simply, and some of it I just don't know exactly.

For traveling waves, the sound field generated depends on a combination of direct field and boundary interference. So the directionality of the speakers and sound propagation come into play.

For standing waves (room modes), directionality doesn't come into the picture (at least not for source radiation), but the position of the source defines the degree of excitation of the various modes. Axial modes behave as plain waves, normal to the walls. Tangential modes behave as wave fronts with regard to the diagonals on a 2-D plain (depends on order), but they form rather complex patterns for higher order modes.
Oblique modes behave as wave fronts with regard to the diagonals in 3-D space, but form very complex patterns for higher order modes.

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

I'm saying all of this to make it clear that exact testing to check equations calls for a lot of (control of) boundary conditions. One must either understand them, or measure them in acoustic laboratories where the field is better known.

Note that all of these resonator formulas assume a lot of boundary conditions, and are based on simple conditions. For exact tuning, one should check this in practice.

Equations for Helmholtz resonators and also for panel traps are nothing more than room acoustic translations of a simple 1 degree-of-freedom mass-spring system. In other words, you can think of it like a small mass, such as a piece of wood, mounted on top of a spring, on a tabletop.

I think I take a slightly different point of view from Thomas on these things. I noticed that Thomas uses a lot of wavelength relationships (which of course is partly correct).

The way slat type Helmholtz resonators are used here is rather broadband. The various slat widths, while certainly useful, are difficult to define theoretically. The law of inertia certainly plays a role in the cavity. The stiffness of the spring will try to smooth it out, but at the same time you also, in fact, get a higher order mass-spring system (multiple degrees-of-freedom).

What I'm saying is: be careful with explanations. I think a lot of systematic testing is needed in order to isolate some of those phenomena. Without having access to such data (published or measured) it's very risky to take certain explanations as fact.

One of the risky things that I notice on the Internet is this: Someone tries to figure out why something happens. He suggests a plausible explanation, which is well thought out. Then, for one reason or another, even though the hypothesis has never been tested, and the originator only suggested it as a possibility that should be investigated, it starts to be taken as fact on the Internet. Just because it's easy to give things a name or simple definition.

Too many well-meant assumptions from searching minds became “facts” like this.

Checking formulas and measuring resonant frequencies based on real-life circumstances is very good, and even advisable for specific applications and use, but risky if used as generalizations of the phenomena, without controlling and understanding all of the boundary conditions.


Eric


I have also have a question for Thomas: Thomas, you said that the efficiency of a Helmholtz or slat resonator can be somehow related to the ratio of open area (slots) to the closed area (slats). Do you have measurements or publications that confirm this?
E.g. “A single 10 ounce Cola bottle at river banks resulted in 5.9 sabins”.

I can't find that backed up, nor do any measurements that I know of confirm this (certainly not as some kind of linear relation). I admit that I have never investigated this, but I do have lots of data, where I can't see this. I also have books that are very vague about it, while going very deep where mathematical approaches can be used. That above-mentioned Cola bottle gives rather impressive results.

What I did test once, was an extensive series of thin perforated steel sheet over rockwool (300 mm and 100 mm thick; surface area of 12 m2 roughly). This testing was done while investigating the acoustic transparency of thin steel sheet for industrial purposes.

I tested between 4.5 % and 70 % perforation. In these tests, nothing related systematically to this ratio (of open to closed area). In fact, what we mainly found was a relationship (that still needs further investigation, since it was not the main purpose of that study) between the closed surface measures and the wavelength as a function of reflection/scattering. Note: all those test were performed by myself in an official university reverb laboratory, in accordance with the ISO 354 standard (standard absorption measurements).


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


-- END OF PARAPHRASE --




- Stuart -

[AVare]

Have I told you this week that you are good man Stuart? If not, you are good man Stuart.

Andre

[Soundman2020]

Thanks, André! Your comments are much appreciated!


- Stuart -

[John Sayers]

thanks Stuart.

I must say I agree with Eric on this statement.

One of the risky things that I notice on the Internet is this: Someone tries to figure out why something happens. He suggests a plausible explanation, which is well thought out. Then, for one reason or another, even though the hypothesis has never been tested, and the originator only suggested it as a possibility that should be investigated, it starts to be taken as fact on the Internet. Just because it's easy to give things a name or simple definition.

Too many well-meant assumptions from searching minds became “facts” like this.

[Soundman2020]

Absolutely! Even though I think Eric meant that at a higher level, I reckon it sums up a lot of acoustic folklore very well too, right down at the level of egg-crates on the walls and carpet on the ceiling.


- Stuart -

[i625]

Now I don't mean to bring back a thread that's years old (disclaimer: I actually do)

But I'm looking into slat Helmholtz resonators right now and stumbled upon this thread. For what it's worth, I've run numbers through the formula:

f_res = 2160*sqrt(s/(d*D*1.2*(s+w)))

where
s is the slot width
w is the slat width
d is the slat depth
D is the cavity depth

and the resonant frequency seemed.. well.. incredibly high for a Helmholtz resonator. I went through acoustics in university and am still studying acoustics, and the general impression that I had (right or wrong) is that Helmholtz resonators are generally for low-mid frequencies.

While we're on the topic of questioning this formula and poking at it from all sorts of angles, I'd like to bring some attention to the 2160 that sits right in front of everything else.

I looked up the formula and happened to stumble across this acoustics textbook on Google books:
Home Recording Studio: Build it Like the Pros By Rod Gervais

and in the text, he mentions that
2160 = c/(2*pi)
where c is the speed of sound

Now, I may be missing something, or this may just be a completely fudged explanation on the author's part, but there is no possible way 343/(2*pi) can be 2160. (But 343*2*pi comes awfully close!)

You might all call me out on using wikipedia as a source, but the Helmholtz resonator frequency is cited to be:

f_res = c/(2*pi)*sqrt(A/(V*L))

where
c is the speed of sound in m/s
A is the cross-sectional area of the opening
V is the volume of the cavity
L is the corrected neck length

From which, I assume, all variants of Helmholtz type equations are derived from. And I think it makes sense that the coefficient out front is supposed to be low, while all the other mass/spring-related terms stay within the square-root.

Just my two cents.
i625

P.S. I like exact numbers, but acoustics has too much jiggery pokery magic for anyone to try to be really exact about anything. People are still trying to make empirical formulas for porous absorbers...!

[Soundman2020]

Hi there "i625". Please read the forum rules for posting (click here). You seem to be missing a couple of things!

and the resonant frequency seemed.. well.. incredibly high for a Helmholtz resonator.

What units are you using? Give an example of what you calculated. You must use the correct units for the equation. If not, you wont get correct answers.

Now, I may be missing something, or this may just be a completely fudged explanation on the author's part, but there is no possible way 343/(2*pi) can be 2160.

Then again, maybe it's just that you aren't understanding what the equation says. Why did you want to mix metric and imperial in your calculations? Nobody said anything about measuring the speed of sound as 343 for the specific equation you are using... You cannot do that. Either use all metric or all imperial, and make sure you are using the right scale for all of your values. Eg. All inches, or all meters, or all feet, or all centimeters, etc. Inserting some numbers as imperial and some as metric will always give you the wrong answer in any equation, and even more so in one that includes a constant. You MUST use the same units as the constant, obviously, but you are not doing that.

Better double-check your assumptions, and your units, and your calculations.

but the Helmholtz resonator frequency is cited to be:

f_res = c/(2*pi)*sqrt(A/(V*L))

where
c is the speed of sound in m/s

Yep... Very true. And notice the units... in that case the constant will not be 2160, and the dimensions could not be imperial either...

And I think it makes sense that the coefficient out front is supposed to be low, while all the other mass/spring-related terms stay within the square-root.

... and you'd be wrong there too! The equation is correct as written, regardless of what you think about it, and it produces the correct results when used correctly, with the correct units. If you do that, then it will ALWAYS give an answer that is correct, but it requires a deeper knowledge of acoustics to determine if such a device can actually be built in practice, and whether or not it would provide useful absorption at the tuned frequency. You could, indeed build a slot-wall that is tuned to 35 Hz if you wanted to, but the dimensions for one that worked efficiently and effectively would be impractical for a real-world studio. To start with, the 1/5th wavelength "rule" would get in the way, as would the 1/10th volume "rule".

Equations work when you use them correctly. And they don't work when you try to mix and match units that are unrelated to each other... They will still produce numbers, but the numbers will not bear any relation to reality. It requires understanding of what you are actually doing to determine if you areu sing the correct numbers.

but acoustics has too much jiggery pokery magic for anyone to try to be really exact about anything.

... and you'd be wrong there too! There's a lot of stuff that can be calculated very exactly in acoustics, and matches reality exactly as well. The equations do, in fact,work. I use them all the time when designing studios. No "jiggery pokery magic" required. That is only needed for people who don't really understand the underlying principles, and are just plugging numbers into equations blindly.

There's still plenty of room for research in acoustics, for sure, but what is known so far is very usefully exact, and the equations that have been found so far are also quite reliable. They can still be refined, certainly, but they are plenty good and plenty accurate for the requirements of a home studio builder.

People are still trying to make empirical formulas for porous absorbers...!

Really? They are? Silly people! They would be much better off just using the existing formula that are known to be correct, instead of "reinventing the wheel" so to speak, by trying to derive them all over again. Hopefully, they will arrive at the same equations that acousticians have already be using for years, quite successfully.


- Stuart -

[Soundman2020]

I've run numbers through the formula: ... f_res = 2160*sqrt(s/(d*D*1.2*(s+w)))... the resonant frequency seemed.. well.. incredibly high for a Helmholtz resonator.

Please post the numbers you actually used there, so we can figure out where your mistake is, and help you get the right answers.

- Stuart -