음향시스템핸드북 보다가.. 질문 하나만 해도 될까요
2011.06.21 12:45
첨부된 그림은 아시다시피 헬름홀쯔 공명기에서 흡음되는 주파수를 구하는 공식입니다.
그런데 책에
"직경이 5 mm, 간격이 100mm, 벽체간격이 200 mm, 깊이가 25 mm 라면 소멸되는 주파수는 153Hz가 된다"
라고 나와있는데 아무리 계산을 해봐도 153 이라는 숫자는 나오지 않고 1503 밖에 안나오거든요;;
저 값들을 어떻게 계산해야
153 이라는 숫자가 나오죠? 제가 뭘 놓친지 잘모르겠네요..ㅎㅎ 부탁드립니다
댓글 9

장호준
2011.06.22 10:26

박근영
2011.06.22 14:00
음향시스템핸드북 49페이지요.. 장호준 님 책 맞는데요..;

장호준
2011.06.29 07:26
책 49페이지입니다.
질문에 다시 인용했던 서적을 찾아보니까, 공식에 잘못된 부분이 있네요. (직경x간격)으로 된 부분이 (직경+간격)이구요. 단위를 mm가 아닌 인치로 적용해야만 하는 공식입니다. 2006년 3차 개정판에 들어간 부분인데, 그동안 누구도 확인을 하지 않았거든요. 실수네요^^
감사.

박근영
2011.06.30 09:25
그래도 계산이 안나오네요...;; 제가 이해를 잘 못하는듯...
죄송하지만 계산하는 수식좀 알려주시면 감사하겠습니다
그리고 저긴 f= 2160 이라고 적혀있고 책엔 f=54140 이라고 적혀있는데 이건 상관없는거죠?

장호준
2011.07.01 10:29
ㅎㅎ 그렇게 중요한건 절대 아닌데, 중요한 부분이 있나보군요. 일단 가지고 계신 책을 사진으로 올려주시면 좋겠습니다. 잘 기억이 안나는데, 54140과 2160은 단위의 차이로 변해지는 계수일겁니다.. 수학이나 공학은 저도 약해서.ㅋㅋ
아래의 사진이 출처입니다.

장호준
2011.07.01 11:48
공식을 엑셀로 만든것입니다. 참조하시길..

장호준
2011.07.01 11:52
학자들 사이에서도 이견이 있네요...

SLAT TYPE HELMHOLTZ RESONATOR FORMULA
3 posts • Page 1 of 1SLAT TYPE HELMHOLTZ RESONATOR FORMULA
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: 20040202 15:45:49 PST
The noticed error was further investigated by the author versus diverse editions of the referred books.

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

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.

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"
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 massspring 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 Qfactor.
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 (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: 20040204 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: 20040204 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 other trained 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.acousticsnoise.com Eric.Desart
 Moderator
 Posts: 2461
 Joined: Tue Feb 10, 2004 4:29 am
 Location: Antwerp, Belgium
Hi Eric:
You probably don't cruise AVS, so I thought I'd mention there's a question at the end of http://www.avsforum.com/avsvb/showthre ... did=367793

formerly HTbuph
Devout buckeye fan!
Registered: Apr 2003
Location: Vero Beach, FL
Posts: 209
Are these correct (from Everest)?
diaphram absorber
f = 170/((m*d)^0.5)
f  frequency
m  panel density (lbs/ft2)
d  airspace depth (in)
perforated panel absorber
f = 200* (p/(d*(t+0.8*D)))^0.5
f  frequency
p  perforation %
d  airspace depth (in)
t  panel thickness (in)
D  hole diameter (in)
Regards
Bob Golds
"The only thing we regret in life is the love we failed to give."
"Be a rapturist  the backward of a terrorist. Commit random acts of senseless kindness, whenever possible"  Jake Stonebender Bob
 Posts: 4237
 Joined: Sun Feb 08, 2004 4:37 am
 Location: Oakville, Ontario, Canada
Bob,
I've little time now, so come back to it later or leave it to other cleverder guys.
Every time I see a formula I must recalculate from Metric to find those constants back:
I'm a metric SI guy.
Out of my head:
The panel formula is correct in such a manner that it assumes the backside of the panel to be an infinite mass and the sound is a plain wave with straight incidence (which is true for axial modes and about at long distance from sources for traveling waves).
If not: as a heavy panel on a light drywall this changes.
Also the resonance frequency is very angle of incidence dependent.
In fact for any resonator one must be careful for the exact tuning when it matters.
All formulas you'll see always assume stylized boundary conditions.
I'll check those things later.
For the panel resonance you can use in the time between my Massspring Excel file on my site.
In fact the formula for a panel resonator is exactly equal as the formula to calculate the massspring of a drywall.
The other one I must check myself. Eric.Desart
 Moderator
 Posts: 2461
 Joined: Tue Feb 10, 2004 4:29 am
 Location: Antwerp, Belgium
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장호준
2011.09.22 11:37
예를 들어 직경이 5mm, 간격이 100mm, 벽체간격이 200mm, 깊이가 25mm 라면 소멸되는 주파수는 155Hz가 된다. (54140는 초당 소리의 속도인 340m를 mm로 바꾼 340,000mm 나누기 2 X 원주율의 값이다. 이것 역시 공식에 의거해 정의된 값이다. 어떤 공간에 온도가 달라서 소리의 속도가 다를 경우 유추해서 이 값을 찾을 수 있다.)
위의 내용이 맞는 내용이 되네요.

plsc45
2011.12.28 16:30
공식까지 공부하시다인 대단하구요
열정이 대단합니다.
공식의 출처가 제 책은 아닌데... 어디에서 나온거죠?