Wrong Helmholtz formula!?

the dreamer · Post by **the dreamer** » Wed Aug 24, 2005 8:49 am

Hi,
I just had a conversation with an acoustician in a german recording board. You know him as Will/Interface at Studiotips.
He pointed out to me, that the corrected Helmholtzspreadsheet is still wrong.

This he gave me as the right one:
fo=c/(2*PI*SQRT(B*D*(d/r+2Δd/r+(1/3)*D/B)))

with:
c = speed of sound[m/sec]
r = slotwidth[m]
w = slatwidth[m]
d = thickness of slat[m]
B = r+w
e = r/B
2Δd = mouthcorrection =2*(-r/PI*ln(sin(PI*e/2)))
D = width of airspace behind the slats[m]

He pointed me to this thread on ST where he pointed this out before:
http://forum.studiotips.com/viewtopic.php?t=1513

And this is the original german thread:
http://homerecording.de/modules/newbb/v ... =47#301436

I wanted to bring this to your attention.
Maybe there is something to examine.
Greetings
Florian

knightfly · Post by **knightfly** » Wed Aug 24, 2005 9:43 am

Florian, thanks; the formula I used for the "corrected" one corresponds with Everest's results in the MHOA, when factoring in the hole depth factor; I'm off to the salt mines in a few, but I copied this to my laptop and if things behave tonite hopefully I'll get a chance to go through it.

Bump this if you think of it so I won't let it slide - thanks... Steve

knightfly · Post by **knightfly** » Wed Aug 24, 2005 9:48 am

Florian, if you get time maybe you could make some comparisons for me - say, 2 or 3 different sets of dimensions calculated with our calculator and the "other correct one", and post your results on this thread? It would be much appreciated, since I'm currently in the midst of multiple, weather-dependent projects - if you can, many thanks... Steve

interface · Post by **interface** » Thu Aug 25, 2005 11:14 am

Here is an Excel file to check the differences of both calculations.

Best wishes
Will

the dreamer · Post by **the dreamer** » Thu Aug 25, 2005 9:12 pm

Will,
Thanks for that handy spreadsheet!
Couldn't you have come up with this a little earlier?

I sat down this morning to follow Steves request for comparisons and tried to calculate a couple. And when I went online, your tool was here

.
I did something wrong anyway, it's many years since I had to deal with maths-stuff. I don't know where I went astray.
I scanned one of my attempts. Maybe you can tell me what went wrong.
The frequency I got for this certain set of parameters is 154,08 Hz whereas calculated with your spreadsheet it gives me 129,96 Hz.
I guess my braincells from about 15 years ago already passed away

Thanks
Florian

interface · Post by **interface** » Thu Aug 25, 2005 11:40 pm

Hi Florian,
the calculation of the mouth-correction is a bit twisted in your formula.

1. "ln(sin(PI*e/2)" needs to be placed in the numerator.
--> have a look again in this way: -r/PI........*ln(sin(PI*e/2))
The result of 2Δd has to be: 0,00928256....

2. check also the result of "sin(pi*e/2)"

Best wishes
Will

interface · Post by **interface** » Fri Aug 26, 2005 5:51 am

Here are measured and calculated results of a SLIT RESONATOR to compare.
Source: Norwegian Department of Telecommunications

Will

the dreamer · Post by **the dreamer** » Fri Aug 26, 2005 6:15 am

interface wrote:Hi Florian,
the calculation of the mouth-correction is a bit twisted ...

Will,
Thanks for helping!

Andrew Steel · Post by **Andrew Steel** » Fri Aug 26, 2005 10:13 am

Hi Will,

Do you have the reference to the original document or the rest of the details like air gap behind the slats, damping material details etc? I would like to have such an example and calculate it myself so that if it matches the graph I know I am doing it reasonably correctly.

Thanks
Andrew

interface · Post by **interface** » Fri Aug 26, 2005 5:16 pm

Hi Andrew,

The adjusted air cavity was exactly 100mm, the fabric was 2.5mm with a flow resistance of 86 Pa*s/m.

Best wishes
Will

interface · Post by **interface** » Fri Aug 26, 2005 7:48 pm

...here is the same calculation which I wrote in Matlab (Transfer Matrix).
...the resolution is a bit better to compare.

Will

AVare · Post by **AVare** » Sat Aug 27, 2005 4:07 am

Thanks Ineerface!

Andre

Andrew Steel · Post by **Andrew Steel** » Sat Aug 27, 2005 7:57 am

Hi Will,

Thank you. Was there no glasswool or anything in the cavity?

Andrew

interface · Post by **interface** » Sat Aug 27, 2005 8:20 am

Andrew Steel wrote:Hi Will,

Thank you. Was there no glasswool or anything in the cavity?

Andrew

Hi Andrew,
There was no glass wool in the cavity.
This is a typical effect by damping only the neck of the resonator.
More damping e.g. with mineral wool would primarily have an influence on the bandwidth and the absorption coefficient.

Will

the dreamer · Post by **the dreamer** » Wed Aug 31, 2005 7:56 am

Hi Steve,
have you had time to investigate this?
Conclusions?
To me it seems to be an important topic as we all refer people to the Helmholtz-calculator all the time! And since there is chance that it is wrong....

Thanks.
Florian