Question about surface impedance

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Chris Whealy - 24 Jun 2004 10:24 GMT

[Cross posted from forum.studiotips.com]

In Cox and D'Antonio's new book on absorbers and diffusers, chapter 1 is
an introduction to the methods used for calculating the absorption
values of porous absorbers.

I have a question about the following statement made in the middle of
page 18 as almost a throw away comment.

"The surface impedance is often split into the real term (resistance)
and imaginary term (reactance). In general, the real term of the surface
impedance is associated with energy losses, and the imaginary term with
phase changes. So a simple inspection of the surface acoustic impedance
can give more insight into the absorbing properties of a material than
the absorption coefficient."

How can more insight be obtained?

I have plotted the real and imaginary parts of the surface impedance
against the final absorption coefficients of the absorber, and I cannot
see an obvious correlation. So I guess I must have missed something.

Can anyone please explain how to interpret the value of the surface
impedance in this manner?

Thanks

Chris W

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The Ghost - 25 Jun 2004 23:37 GMT

> [Cross posted from forum.studiotips.com]
>
[quoted text clipped - 24 lines]
>
> Chris W

Take the real and imaginary parts of the surface impedance and use
them to compute the normal-incidence sound power reflection and sound
power transmission coefficients (see Kinsler and Frey for the
equations). Then plot the calculated transmission and reflection
coefficients against your so-called "final absorption coefficients"
and you will get the correlation that you seek.

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Chris Whealy - 28 Jun 2004 13:53 GMT

> Take the real and imaginary parts of the surface impedance and use
> them to compute the normal-incidence sound power reflection and sound
> power transmission coefficients (see Kinsler and Frey for the
> equations). Then plot the calculated transmission and reflection
> coefficients against your so-called "final absorption coefficients"
> and you will get the correlation that you seek.

Thanks, I'll give that a try. However, the original statements seems to
imply that information can be obtained by direct interpretation of the
real and imaginary parts of the surface impedance.

Maybe this was the extra "undocumented" step...

Thanks

Chris W

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

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The Ghost - 29 Jun 2004 01:45 GMT

> > Take the real and imaginary parts of the surface impedance and use
> > them to compute the normal-incidence sound power reflection and sound
[quoted text clipped - 8 lines]
>
> Maybe this was the extra "undocumented" step...

Possibly. I don't have the book. Another possibility is that the
author is referring to normalized impedance. So you might try
normalizing the real and imaginary ports of the surface impedance by
the impedance of air. I would think that normalized impedances close
to 1+j0 would be correlated with transmission (and high absorption)
whereas normalized impedances whose real parts are significantly above
or below 1 and normalized impedances having large imaginary parts
would be correlated with reflection (and low absorption).

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Chris Whealy - 29 Jun 2004 10:30 GMT

> Possibly. I don't have the book.

Firstly, may I strongly recommend you get Cox and D'Antonio's book.
Apart from the odd cryptic statement or two, it is very well written,
and clearly explains not just the theoretical side of absorber and
diffusor theory, but also the practical application of the theory.

If you don't mind not having the printed book in your hand, you can
download it as an eBook from the publishers here:
http://www.ebookstore.tandf.co.uk/html/moreinfo.asp?BookID=536908926

> Another possibility is that the
> author is referring to normalized impedance. So you might try
> normalizing the real and imaginary ports of the surface impedance by
> the impedance of air.

In all the articles I've read by Trevor Cox, he's usually pretty clear
about what he means. I don't think he would have assumed the statement
means normalized impedance without actually saying so (but I could be
wrong here).

> I would think that normalized impedances close
> to 1+j0 would be correlated with transmission (and high absorption)
> whereas normalized impedances whose real parts are significantly above
> or below 1 and normalized impedances having large imaginary parts
> would be correlated with reflection (and low absorption).

The imaginary part of the impedance (for the surface of a porous
absorber) tends to start out very negative (E.G. << -20,000) for low
frequencies and then climb and cross zero around the 1KHz to 4KHz range.
It does not tend to become to large in the positive direction.

I don't think the correlation is as simple as saying large imaginary
part equals low absorbency. But at the moment, I haven't been able to
spend the time to look at it more closely.

I have also posted this question on the Studio Tips acoustics news
group. See http://forum.studiotips.com/viewtopic.php?t=705

There is another statement in the book (Section 3.6.2, pg 81) in which
the imaginary part (the reactance) is correlated with the addition of
"virtual" mass to the absorber due to the viscous boundary effects
created as air flows through the pores of the absorber. This does shed a
bit more light on the interpretation of the imanigary part of the
impedance, but it is also related to phase change in a manner that I
haven't fully understood yet.

When I get some time, I will try the suggestions you have made.

Regards

Chris W

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

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The Ghost - 30 Jun 2004 01:12 GMT

Chris Whealy <chris.whealy.NO@SPAMsap.com> wrote in message news:<cbrcs4>

> Firstly, may I strongly recommend you get Cox and D'Antonio's book.
> Apart from the odd cryptic statement or two, it is very well written,
> and clearly explains not just the theoretical side of absorber and
> diffusor theory, but also the practical application of the theory.

Thanks for the recommendation, but I don't have any interest in this
area. The suggestions that I made are based on my knowledge of
impedance matching in general and are not based on any specific
experience that I have with sound absorbers. I thought that my
suggestions might be helpful to you in resolving the issue that you
raised. If they do, great. If not, perhaps someone else can offer
other suggestions. Perhaps you should consider writing the authors
for an explanation, if/when you find the time.

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Chris Whealy - 30 Jun 2004 09:42 GMT

> Thanks for the recommendation, but I don't have any interest in this
> area. The suggestions that I made are based on my knowledge of
[quoted text clipped - 4 lines]
> other suggestions. Perhaps you should consider writing the authors
> for an explanation, if/when you find the time.

Thanks for your input. And yes, I have already mailed both the authors
(on a slightly different question). I am disappointed to report that I
have not received any reply from Peter D'Antonio and Trevor Cox
expressed very little interest in answering my question.

I'll report back any progress I make in answering this question.

Chris W

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

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Natural Science Forum / Physics / Acoustics / June 2004

Question about surface impedance