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Helmholtz absorber calculation spreadsheet

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Anonymous
May 14, 2004 10:21:54 PM

Archived from groups: rec.audio.pro,rec.audio.tech,alt.sci.physics.acoustics (More info?)

I have just completed V1.0 of a spreadsheet to calculate the absorption
curve of a slotted or perforated Helmholtz absorber.

This type of calculation is more useful (IMHO) than simply calculating
the resonant frequency of a Helmholtz resonator, because the absorption
curve will give you an idea of the bandwidth over which absorption
occurs, rather than just a simple frequency value.

This spreadsheet requires the use of the Excel Analysis ToolPak. It
will all go horribly wrong if you don't have this feature switched on!
Please follow the instructions on the download page in order to install
this particular feature of Excel.

This is available for free download from
http://www.rmmpnet.org/members/ChrisW/index.html

Any feedback, comments or constructive criticism would be appreciated.

The reviewers have already made suggestions for improvement, and I am
working on these for V1.1

Thanks for looking,

Chris Whealy

--
The voice of ignorance speaks loud and long,
but the words of the wise are quiet and few.
--
May 14, 2004 10:43:43 PM

Archived from groups: rec.audio.pro,rec.audio.tech,alt.sci.physics.acoustics (More info?)

"Chris Whealy" <chris.whealy.NO@SPAMsap.com> wrote in message
news:c82v7i$m51$1@news1.wdf.sap-ag.de...
> I have just completed V1.0 of a spreadsheet to calculate the absorption
> curve of a slotted or perforated Helmholtz absorber.
........
> Any feedback, comments or constructive criticism would be appreciated.

Thanks - very interesting. Can you give the physical explanation of the
multiple peaks of absorption for the slotted case?

Tony Woolf
Anonymous
May 16, 2004 3:38:58 AM

Archived from groups: rec.audio.pro,rec.audio.tech,alt.sci.physics.acoustics (More info?)

Tony wrote:
> Thanks - very interesting. Can you give the physical explanation of the
> multiple peaks of absorption for the slotted case?

The complexity of the absorption curve is controlled by the combination
of panel thickness and cavity depth. It is not affected by the slot
width or absorber flow resistivity. These latter values simply control
the level of absorbency, not the absorbency profile.

The behaviour of a Helmholtz absorber is very much like the effect you
get when you blow over the top of bottle. You hear a specific frequency
that corresponds to the ratio of air mass in the neck of the bottle, and
the compliance (or springiness) of the air in the body of the bottle.
In mechanical terms, this is the same type of system as a mass
oscillating on a damped spring. The air in the neck of the bottle is
like the mass, and the air in the body of the bottle is like the damped
spring.

The equations implemented by the spreadsheet use a transfer matrix to
calculate the overall absorption. This starts by calculating the
impedence at the top of the air cavity, then using this value, to
calculate the impedance at the top of absorber.

The value at the top of the absorber is then used to calculate the
overall absorption of the system at a given frequency.

As far as answering your question is concerned, all I can say is that
predicted absorption peaks must be due to interference between the
resonant frequency of the air in the "bottle neck" (the air space
created due to the panel thickness), and the resonant frequency
determined by the cavity depth.

Chris W

P.S. If you don't have Cox and D'Antonio's book (from which I got the
implementation of these formulae), then might I suggest that you get it!
:-)

--
The voice of ignorance speaks loud and long,
but the words of the wise are quiet and few.
--
Related resources
Anonymous
May 16, 2004 2:08:26 PM

Archived from groups: rec.audio.pro,rec.audio.tech,alt.sci.physics.acoustics (More info?)

Chris Whealy wrote:
> I have just completed V1.0 of a spreadsheet to calculate the absorption
> curve of a slotted or perforated Helmholtz absorber.
> The reviewers have already made suggestions for improvement, and I am
> working on these for V1.1
> Thanks for looking,
>
> Chris Whealy
>

In the Slotted Absorber there were terms for panel thickness and slot width, but nothing for the
distance between slots. Is there something I've overlooked ?
Anonymous
May 17, 2004 1:56:06 PM

Archived from groups: rec.audio.pro,rec.audio.tech,alt.sci.physics.acoustics (More info?)

Brian Marston wrote:
> In the Slotted Absorber there were terms for panel thickness and slot
> width, but nothing for the distance between slots. Is there something
> I've overlooked ?

The distance between holes is necessary in the case of a peforated
absorber which is a 2D arrangement of holes, each functioning
independently. In this case the open area of the panel is calculated using:

eta = (Pi() * a^2) / D^2

Where:
eta = %age open area
a = hole radius
D = repeat distance

However, for a slotted absorber, the open area is calculated as follows:

eta = (0.0465 * 4 * d) / (Pi() * 0.05^2)

Where:
eta = %age open area
d = slot width

Here, the open area is calculated using only the slot width.

This is the formula implemented by Cox and D'Antonio in Script 6.2 in
Appendix B of their book. On the one hand I have no reason to doubt the
accuracy of their formulae, but on the otherhand, I cannot adequately
explain it's derivation.

But I'm working on it...

Chris W

--
The voice of ignorance speaks loud and long,
but the words of the wise are quiet and few.
--
Anonymous
May 17, 2004 5:17:43 PM

Archived from groups: rec.audio.pro,rec.audio.tech,alt.sci.physics.acoustics (More info?)

Brian Marston wrote:
> In the Slotted Absorber there were terms for panel thickness and slot
> width, but nothing for the distance between slots. Is there something
> I've overlooked ?

I've had a closer look at this situation, and it appears that I have
hard-coded the parameter for the distance between the slots. I think
that the MATLAB script that I reimplemented had a hardcoded value
instead of a variable name, and I just copied the value into the
spreadsheet. (yeah, yeah, I'll pay more attention next time...)

As currently implemented, this distance is set at 50mm. I will correct
the spreadsheet and reissure it within the next day or two.

Sorry if this has caused any inconvenience.

Chris W

--
The voice of ignorance speaks loud and long,
but the words of the wise are quiet and few.
--
Anonymous
May 17, 2004 6:11:48 PM

Archived from groups: rec.audio.pro,rec.audio.tech,alt.sci.physics.acoustics (More info?)

Brian Marston wrote:
> Chris Whealy wrote:
>
>> I have just completed V1.0 of a spreadsheet to calculate the
>> absorption curve of a slotted or perforated Helmholtz absorber.
>> The reviewers have already made suggestions for improvement, and I am
>> working on these for V1.1
>> Thanks for looking,
>>
>> Chris Whealy
>>
>
> In the Slotted Absorber there were terms for panel thickness and slot
> width, but nothing for the distance between slots. Is there something
> I've overlooked ?
>

The MATLAB scripts that I reimplemented used the following derivations
for the panel porosity (open area)

Perforated panel:

epsilon = (Pi() * a^2) / D^2

Where:
epsilon = porosity
a = hole radius
D = repeat distance

Slotted panel:

epsilon = (0.0465 * 4 * d) / (Pi() * 0.05^2)

Where:
epsilon = %age open area
d = slot width

I believe that the 0.05^2 term in the above equation should be D^2,
where D is the distance between the slots. I was expecting a variable
to be at this position in the formula, not a hard coded value.

As currently implemented, this distance is hard-coded at 50mm. I will
correct the spreadsheet and re-issue it within the next day or two.

Sorry if this has caused any inconvenience.

Chris W
--
The voice of ignorance speaks loud and long,
but the words of the wise are quiet and few.
--
!