# Talk:Acoustic impedance

This article has weaknesses. Is this the standard way to present this material? It feels show-off-y rather than trying to be useful. 99% of readers can get a useful understanding of impedance without hitting them over the head at the very beginning with a confusing Fourier/Laplace duality and a similar time domain / frequency domain schizophrenia. In my opinion, this kind of information, if included at all, should be moved to the end--i.e. after the useful stuff-- and the reader should be gently led into it as the underpinnings of a frequency-domain interpretation. 108.51.128.84 (talk) 14:15, 17 March 2017 (UTC)

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The description of the different (?) concepts of characteristic impedance, specific impedance, and other impedances (?) needs to be completely clear, and only then assigned usually employed symbols for the concepts. The article must not assume the reader's knowledge of the meanings of different Z's, neither define stuff in terms of them, just mention them as frequently used symbols. Symbol use is not consistent around the world, and thus sentences like the characteristic acoustic impedance ${\displaystyle Z_{0}}$... should rather be the characteristic acoustic impedance, (often denoted ${\displaystyle Z_{0}}$). As as my understanding of this is not completely clear, I cannot make the improvement, and I ask someone who knows to do it. 78.91.40.207 (talk) 17:47, 6 February 2009 (UTC)

Distinction has to be made between:

• the characteristic acoustic impedance ${\displaystyle Z_{0}}$ of a medium, usually air (compare with characteristic impedance in transmission lines).
• the impedance ${\displaystyle Z\ }$ of an acoustic component, like a wave conductor, a resonance chamber, a muffler or an organ pipe.
This seems to differs from the electrical definition of impedance in that wave conductors and organ pipes would be considered transmission lines, not components, and would have a characteristic impedance. — Omegatron 18:26, August 26, 2005 (UTC)

Very well observed, Omegatron: the input impedance of a wave conductor will vary with its termination and a great deal of its impedance is explained by transmission line behavior. Think about it in physical terms: you can in fact "look through" a wave conductor. A sound wave within the conductor will be affected by the reflection at the end of the tube and the measured impedance at the entrance will vary accordingly. A closed-end organ pipe is maybe an exception, since its impedance can be expressed as a "fixed" (but still cyclical) component. The termination finds an electrical analogy in a short circuit. In reality however, the acoutical short circuit in an organ pipe is not ideal. The closed end is not optimal rigid and often vibrates. The sound wave will therefore loose some energy and will not be 1:1 reflected.Witger 06:45, 20 September 2005 (UTC)

I think the analogy is actually closer. Electrical transmission lines and impedances are idealisms anyway. I believe a closed and open organ pipe is equivalent to a short circuit or open circuit terminated transmission line. Of course there is no such thing as a perfect short or perfect open, and some leakage will occur. — Omegatron 02:15, 21 September 2005 (UTC)

Hi Omegatron! An open end organ pipe is terminated by what is called a radiation impedance. The term is well known in RF applications. In acoustics it finds applications in solving noise problems in air conditioning systems. The radiation impedance has been also mathematically derived for an ideal sound source in a flat wall (as far as I remember with very complicated Bessel functions). The radiation impedance depends on the radius of the pipe and its proportion to the wavelength. Also exhaust pipe systems of cars benefit from the radiation impedance: this is (one) of the reasons why very noisy engines have several exhaust outlets (though maybe one preceeding muffler casing) and why the tail pipe is usually the longest length of the muffler system. In the particular case of an exhaust pipe: if the open end would be really a "open circuit" with infinite impedance, then the tail pipe wouldn't add up in the insertion loss of the system.Witger 07:35, 21 September 2005 (UTC)

Very cool. That should probably be added to the article. — Omegatron 13:57, 21 September 2005 (UTC)

Is it safe to say that characteristic impedance doesn't change with frequency? I would think that there are limits to the sounds that can go through air, but maybe that's a different concept? Does air have an acoustic absorption spectrum or something when you get above ultrasound? — Omegatron 03:11, 3 May 2007 (UTC)

-Yes characterisic impedance is usually assumed be a constant under normal acoustic conditions. It is not usually considered to be frequency dependent. Unless the the acoustic variables (pressure, density, etc) become extremely large with respect to the ambient characteristics, one can assume that it is constant. There should be a dedicated page on absorption in Air as it can be very complex. emh203 10:57 7, May 2007 (EST)

There is a table of other materials at [1] in rayles that we could convert and include. — Omegatron 03:34, 3 May 2007 (UTC)

As soon as I get some time :-) , there needs to be some more ellaboration of all the types of impedance used in acoustics. This topic is a large source of confusion. I'll try to get everything with proper citations, etc. What is on the page is mostly correct but there needs to be some discussion about how and when the relationships are valid and where the relationships come from. There also needs some topics added such as Radaition impedance of a source. emh203 10:57 7, May 2007 (EST)

## Frequency dependence of characteristic impedance

The characteristic impedance of a fluid is density * sound speed. In a dispersive medium the sound speed varies with frequency and all real media are slightly dispersive. As density is independent of frequency it follows that the characteristic impedance must vary with frequency. Thunderbird2 17:05, 12 July 2007 (UTC)

In air, I believe velocity becomes spatially variable at frequencies above 26KHz (dispersion transition frequency) - below that frequency, it remains essentially constant. I've not seen any data to date that suggests below this frequency, sound velocity varies signficantly - assuming typical conditions with respect to atmospheric pressures and molecular composition. —Preceding unsigned comment added by 71.234.32.89 (talk) 22:46, 25 February 2010 (UTC)

## Impedance confusion

There seems to an error relating to acoustic impedance here. Taking the Kinsler 'fundamentals of acoustics' book as authority (sect 10.4): Rayl is the unit of specific (and characteristic?) acoustic impedance,z, not acoustic impedance, Z, (the units Pa.s/m in http://en.wikipedia.org/wiki/Rayl support this - that section makes this mistake too though). The unit of acoustic impedance is the acoustic ohm (Pa.s/m^3)

Also, looking at the external link http://www.sengpielaudio.com/RelationshipsOfAcousticQuantities.pdf the term acoustic impedance there actually refers to specific acoustic impedance. Presumably people often use the term 'acoustic impedance' to mean 'specific acoustic impedance', but since both are defined here we should keep them distinct. I'm still fairly new to acoustics (and wikipedia), so would appreciate comment before I amend the article. Pgj98r (talk) 11:34, 26 February 2008 (UTC)

## Complex impedance

The section on complex impedance is self-contradictory and the edit of 23:25, 25 February 2010 is definitely wrong. When I get the chance I will try to figure out what actually should be said about complex acoustic impedances, but failing that the paragraph added in February should be removed unless someone has an objection.

I was reading this page, and realized that the previously mentioned paragraph was completely wrong and saw this note. I went ahead and deleted it. —Preceding unsigned comment added by Ejeffrey (talkcontribs)

This section is still contains errors and misleading statements as of Feb. 21, 2011. For instance, the particle velocity and pressure are in quadrature phase. When one is at an extremum, the other is zero; it is just like kinetic and potential energy in the pendulum problem. There is a phase difference between the two quantities; what I think the section intends to say is that the phase relationship does not normally vary. However, it can, and in some special media, the displacement (velocity) can actually be in reverse phase with the applied force (pressure), giving an effectively negative mass density. Such effects can occur without violating causality. This page largely pertains to dispersionless acoustics far from resonance, and should be corrected accordingly. — Preceding unsigned comment added by Rwestafer (talkcontribs) 18:19, 21 February 2011 (UTC)

## Phase

I deleted a paragraph of uncited reasoning about the phase. Once the conclusions will be convincingly backed up by reliable references, the paragraph may be restored. --Maxim 62.149.15.226 (talk) 18:05, 25 October 2011 (UTC)

## "Molecules" and "particle velocity"

I don't see the point of mentioning molecules or particles in the introduction. A basic understanding does not requite reference to atomic theory, and in fact acoustics was well developed in the 19th century before Einstein's work on Brownian motion firmly established atomic theory. The fact that acoustics did not establish atomic theory shows that atomic theory is not needed to understand acoustics. One needs to think of mater as a bulk medium to understand sound, but the reader should be saved the extra effort of deriving bulk properties from the properties of the constituent molecules. "Particle velocity" should be written as something like velocity of the medium or matter velocity. David R. Ingham (talk) 18:14, 23 March 2013 (UTC)

## Electrical impedance

It seems that the analogy to electrical impedance should be mentioned peripherally but early on, because some people such as electrical engineers are familiar with electrical impedance but not with acoustic impedance. David R. Ingham (talk) 18:24, 23 March 2013 (UTC)

## Complex resistance

Maggyero, how can you write "Acoustic impedance is the complex representation (also called analytic representation) of acoustic resistance" when acoustic resistance is one component of acoustic impedance. The whole cannot be a representation of the part. By the way, you should only link an item once per WP:OVERLINK. This is not the only example, Pa and other units seem to have ended up linked numerous times. SpinningSpark 04:36, 14 November 2014 (UTC)

Spinningspark, if you look at the article Analytic signal you will see that the analytic representation fa(t) of a signal f(t) is defined as:
${\displaystyle f_{\mathrm {a} }(t)=f(t)+i{\mathcal {H}}[f](t),}$
where ${\displaystyle {\mathcal {H}}}$[f] is the Hilbert transform of f. So the whole can be a representation of the part.
Since acoustic resistance R is defined as:
${\displaystyle R(t)=\left[p*Q^{-1}\right]\!(t),}$
where
• ${\displaystyle *}$ is the convolution operator;
• Q −1 is the convolution inverse of Q,

the analytic representation of acoustic resistance Ra is called acoustic impedance and denoted Z:

${\displaystyle Z(t)=R_{\mathrm {a} }(t)=R(t)+i{\mathcal {H}}[R](t)=R(t)+iX(t)={\frac {1}{2}}\!\left[p_{\mathrm {a} }*\left(Q^{-1}\right)_{\mathrm {a} }\right]\!(t).}$
Okay for your second remark, I will remove the unnecessary links for the units.
Maggyero (talk) 12:04, 14 November 2014 (UTC).
Impedance is not a signal. That's a very odd way of looking at it. We just wouldn't define it that way in electrical engineering, please provide a source. ${\displaystyle p(\mathbf {r} ,\,t)}$ and ${\displaystyle U(\mathbf {r} ,\,t)}$ are time varying instantaneous values, right? So if they are not in phase (and there is no distinction to impedance if they are) then ${\displaystyle R(\mathbf {r} ,\,t)}$ is also a time varying quantity. Furthermore, R is dependent on the applied sound which is a nonsense. R should be a constant dependent only on material and geometry, not on time. Even if we take p and U as being RMS values, their ratio is the magnitude of Z, not the real part of Z. SpinningSpark 12:58, 14 November 2014 (UTC)
I don't think Maggyero is arguing that impedance is a signal. He is just saying that acoustic impedance is usually defined as the ratio of two complex quantities, both of which are independent of time, and equal to the Fourier transforms of the respective time domain waveforms. He is correct. Dondervogel 2 (talk) 16:26, 14 November 2014 (UTC)
I agree that impedance is the ratio of two complex quantities that are independent of time, but that is not what Maggyero has written, either here or in the article. Writing x(t) means that x is a function of t. Z=p(t)/U(t) is wrong, we don't want p(t), we want p(s) or p(iω). Further, Z=R+iX we all agree. To then say that Z is the complex representation of R is completely wrong. R is a component of Z, not another representation of it. SpinningSpark 17:03, 14 November 2014 (UTC)
OK, now I understand the source of the confusion. Is it perhaps the case that, while p'(t) and u'(t) are both functions of time, their ratio is not? I am using the prime here to denote the analytic function f'(t) = f(t) + i*H[f(t)]. Dondervogel 2 (talk) 17:28, 14 November 2014 (UTC)
Well Maggyero has written R=p/u, not R=p'/u' or R'=p'/u', but that wasn't my central point. My point is that saying the complex representation of acoustic resistance is Z is just plain confusing. Calling that quantity R is just playing with semantics, it gives the two quantities the same letter but that still doesn't mean that one is a representation of the other. Z contains an element that is just not present in R in any representation. I return to my request to provide a source that presents the information in this way. There are numerous books on acoustics and it can easily be seen that this is not a normal presentation of the material. Wikipedia is meant for a general readership, not the small minority who understand how to use hamiltonians. SpinningSpark 10:56, 15 November 2014 (UTC)
Spinningspark, in fact we are both right. Impedance can be defined in 3 different ways: as the Laplace transform or the Fourier transform or the analytic representation of the time domain resistance. In the time domain we have:
${\displaystyle R(t)=\left[p*Q^{-1}\right]\!(t),}$
where
• ${\displaystyle *}$ is the convolution operator;
• Q −1 is the convolution inverse of Q.
So the impedance is given by:
${\displaystyle Z(s){\stackrel {\mathrm {def} }{{}={}}}{\mathcal {L}}[R](s)={\frac {{\mathcal {L}}[p](s)}{{\mathcal {L}}[Q](s)}}={\frac {{\hat {p}}(s)}{{\hat {Q}}(s)}}=R(s)+iX(s),}$
${\displaystyle Z(\omega ){\stackrel {\mathrm {def} }{{}={}}}{\mathcal {F}}[R](\omega )={\frac {{\mathcal {F}}[p](\omega )}{{\mathcal {F}}[Q](\omega )}}={\frac {{\hat {p}}(\omega )}{{\hat {Q}}(\omega )}}=R(\omega )+iX(\omega ),}$
${\displaystyle Z(t){\stackrel {\mathrm {def} }{{}={}}}R_{\mathrm {a} }(t)={\frac {1}{2}}\!\left[p_{\mathrm {a} }*\left(Q^{-1}\right)_{\mathrm {a} }\right]\!(t)=R(t)+iX(t),}$
where
• ${\displaystyle {\mathcal {L}}}$ is the Laplace transform operator;
• ${\displaystyle {\mathcal {F}}}$ is the Fourier transform operator;
• subscript "a" is the analytic representation operator;
• in Z(s), R(s) is not the Laplace transform of the time domain acoustic resistance R(t), Z(s) is;
• in Z(ω), R(ω) is not the Fourier transform of the time domain acoustic resistance R(t), Z(ω) is;
• in Z(t), R(t) is the time domain acoustic resistance and X(t) is the Hilbert transform of the time domain acoustic resistance R(t), according to the definition of the analytic representation.
I have just finished improving the article to make all that clearer, you can have a look.
Maggyero (talk) 19:50, 4 March 2015 (UTC).

## rayl or Rayl?

Is the unit name (or symbol) spelt "rayl" or "Rayl"? See discussion on this talk page. Dondervogel 2 (talk) 23:33, 6 December 2014 (UTC)

## Unit confusion

There is confusion over the units in the opening paragraph. It says the units of acoustic impedance are N·s/m3 or rayl/m2 which means 1 rayl = 1 N.s/m. It then says that the units of specific acoustic impedance are Pa·s/m or rayl. Now Pa.s/m is exactly equivalent to N·s/m3 (1 Pa = 1 N/m2) so they can't both be simultaneously equal to 1 rayl/m2 and 1 rayl. The Wikipedia page for the rayl says it's equal to 1 Pa.s/m so something is inconsistent. What are the correct units? 130.246.58.72 (talk) 11:24, 27 October 2017 (UTC)