Talk:Sound intensity

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Although the definition given here can be found in many books (e.g. Norton and Karczub), the time integration is misleading. Active sound intensity is quantity in the frequency domain. By the definition in this page, active intensity is a number independent of time and frequency such that the intensity 'on 1000Hz' is not defined. The reason that the definition has stuck is that many accousticians 'assume that the singals are sine waves' rather than taking a proper Fourier transform. In practice, sound is a broadband phenomenon so I think we should change to a proper definition.

I would suggest that the discussion is started with the definition of the energy flux: $p(t)\cdot v(t)$, and then generalized to the form which is used in measurements: the cross-spectrum between p and v.

Normally, I conclue my comments on wikipedia with the comment that I'm not an expert and I am reluctant to change anything. Since acoustics is my job, I'd be happy to write this one if anyone agrees the current version is misleading.

People seem to get confused by dB vs linear units. When you express sound intensity in dB (giving "sound intensity level"), the physical quantity being expressed is still intensity. dB is just a convenient way of expressing the relative intensity in a convenient, dimensionless form. It's like a change of units. Instead of expressing intensity in watts per square meter, you could express it in horsepower per square foot. Although that would be a strange choice, it doesn't change the physical quantity being expressed.

Note that sound pressure level also started out as a measure of power, not pressure, since the formula is $L_{\mathrm {p} }=20\,\log _{10}\left({\frac {p_{1}}{p_{0}}}\right)=10\,\log _{10}\left({\frac {p_{1}^{2}}{p_{0}^{2}}}\right)$ , and p² is proportional to the power per unit area of the sound wave. If the acoustic impedance were always constant, dB-SPL would be a measure of intensity, even though it is based on the pressure. Of course, the impedance is not always constant, so in practice dB-SPL indicates what the intensity would be if the impedence were fixed.

In practice, it is important to distinguish between dB-SIL, dB-SPL, dB-SWL, etc., because they have different reference levels and because different measurement methods may be implied by the choice of units. Obviously if you have a detector which directly measures pressure, it makes more sense to express the results in dB-SPL than in dB-SIL.--Srleffler 04:27, 28 November 2005 (UTC)[reply]

As I've said on some other acoustics pages - it's important to remember that sound intensity is a vector and sound pressure is a scalar. So it is not generally true to say that "If the acoustic impedance were always constant, dB-SPL would be a measure of 'intensity'" because one requires the specification of direction and the other doesn't.—The preceding unsigned comment was added by Richardng (talk • contribs) .

Strength

Wikipedia policy discourages linking directly to a disambiguation page, unless it's the amorphousness of the term that's under discussion. "Strength" appears to be used in a somewhat-specific sense in the article, but I can't figure out what precisely is meant, and which article I should re-link the word to. Signal strength? Would someone with expertise help, please? Sanguinity 19:23, 24 August 2006 (UTC)[reply]

Following the lead set on "Intensity", I'm redirecting "strength" to the wiktionary entry, and will do the same on the other sound-measurement pages (phon, sound pressure). Again, if a particular sense of "strength" is meant, please re-link as appropriate. Sanguinity 18:37, 25 August 2006 (UTC)[reply]

Bil is the unit of ? Sourabh Suman (talk) 17:51, 25 September 2016 (UTC)[reply]

Intensity at r = 0?

I came to this page already familiar with the inverse square relationship between distance and intensity, hoping to find something that could be of use to me in a little simulation I'm running regarding interference. Anyhow, that inverse square relationship makes the intensity shoot off to infinity as you approach zero, which doesn't seem right (I mean, I can stick a buzzing fly in my ear and I certainly won't suffer any hearing loss as a result). Surely there is some way to calculate intensity starting from the source. I think this article could use something that would help explain that. Eccomi (talk) 19:50, 18 May 2008 (UTC)[reply]

Been a while since I've done the math, but I'm pretty sure that you take the total power and divide by the total area of the sound source. For instance, a vibrating 12in loudspeaker with a 60W driver would have a surface area of

\pi r^{2}=0.072m^{2}

. The max intensity would then be 60W divided by this area. I think. Like I said, it's been a while.Gunblader928 (talk) 00:05, 24 January 2013 (UTC)[reply]

Where you're going wrong is that you are assuming a point source and that assumption breaks down when the distance from the source becomes comparable to the actual size of the source. -—Kvng 15:48, 26 January 2013 (UTC)[reply]

Know about Units.

'Bil' is the unit of ? Sourabh Suman (talk) 17:53, 25 September 2016 (UTC)[reply]

Reference 6...

...is a dead link — Preceding unsigned comment added by 84.165.102.151 (talk) 07:28, 11 July 2017 (UTC)[reply]

More information for "Measurement" section

First of all I would like to disclose that I work for Microflown Technologies, a sensor manufacturer company. I've tried to contribute to the page by adding some general information mainly extracted from a journal publication from Finn Jacobsen, who established the theoretical foundation for both types of transducers able to measure sound intensity (p-p and p-u probes). The change was rejected but I still think that this is rather objective information that should be available on wikipedia. This was the contribution:

Sound pressure and acoustic particle velocity can be directly acquired using a sound intensity p-u probe comprising a microphone and a particle velocity sensor, or estimated indirectly by using a p-p probe to approximate acoustic particle velocity from the gradient between two microphones.

Pressure-based measurement methods are widely used in anechoic conditions for noise quantification purposes. The bias error introduced by a p-p probe can be approximated by^[1]

${\widehat {I}}_{n}^{p-p}\simeq I_{n}-{\frac {\varphi _{\text{pe}}\,p_{\text{rms}}^{2}}{k\Delta r\rho c}}=I_{n}{\biggl (}1-{\frac {\varphi _{\text{pe}}}{k\Delta r}}{\frac {p_{\text{rms}}^{2}/\rho c}{I_{r}}}{\biggr )}\,,$

where $I_{n}$ is the “true” intensity (unaffected by calibration errors), ${\hat {I}}_{n}^{p-p}$ is the biased estimate obtained using a p-p probe, $p_{\text{rms}}$ is the root-mean-squared value of the sound pressure, k is the wave number, $\Delta r$ is the microphone separation distance, $\rho$ is the density of air, and c is the speed of sound. This expression shows that the effect of a given phase error is inversely proportional to the frequency and the microphone separation distance and is proportional to the ratio of the mean square sound pressure to the sound intensity^[2]. If this ratio is large then even the small phase errors mentioned earlier will give rise to significant bias errors. In practice, they cannot be utilized when the pressure-intensity index is high, which limits the use of p-p intensity probes in environments with high levels of background noise or reflections.

On the other hand, the sound intensity is simply the time average of the instantaneous product of the pressure and particle velocity signals,^[3]

$I_{n}=<p\,u_{n}>_{t}={\frac {1}{2}}{\text{Re}}\{{pu_{n}^{*}}\}$

where $<>_{t}$ indicates time averaging, and the latter expression is based on the complex representation of harmonic variables. The bias error introduced by a p-u probe can be approximated by^[1]

${\hat {I}}_{n}^{p-u}={\frac {1}{2}}{\text{Re}}\{{p{\hat {u}}_{n}^{*}}\}={\frac {1}{2}}{\text{Re}}\{{pu_{n}^{*}{\text{e}}^{-{\text{j}}\varphi _{\text{ue}}}}\}\simeq I_{n} \varphi _{\text{ue}}J_{n}$

where ${\hat {I}}_{n}^{p-u}$ is the biased estimate obtained using a p-u probe, $J_{n}$ is the reactive intensity and $\varphi _{\text{ue}}$ is the p-u phase mismatch introduced by calibration errors. Therefore, the phase calibration is critical when measurements are carried out under near field conditions, but not at all critical if the measurements are carried out in the far field^[1]. The “reactivity” (the ratio of the reactive to the active intensity) indicates whether this source of error is of concern or not. However, it should be noted that p-u intensity probes are unaffected by the pressure-to-intensity index, enabling the estimation of propagating acoustic energy despite unfavorable testing conditions.

Fernandez.microflown (talk) 14:39, 15 July 2019 (UTC)[reply]

Pinging Viewmont Viking who removed the content. Personally I don't see much wrong with the content from a WP:COI point of view (there are some style issues that need addressing, such as "it should be noted", "simply", and similar editorial comments that are unsuitable for Wikipedia), but if these are indeed the standard probes used to measure sound intensity, then they will be covered by numerous other sources, and there should be no need to rely on ones associated with Microflown Technologies. Huon (talk) 23:06, 4 October 2019 (UTC)[reply]

I do not see a conflict either, so I agree there is no reason to remove the content on those grounds, but I find the text confusing and I think it needs improvement. For example, while it is correct to state that sound intensity is the time average of sound pressure p and particle velcocity u, it is not correct to write this as (1/2) Re(p u*), because these are not the same p and u. In the time average they are real quantities, in the time domain. In the second form they seem to be complex quantities (in the frequency domain?). Further, a p-p does not give particle velocity directly but particle acceleration, which can then be converted to velocity in a simple manner in the frequency domain. If the presentation is improved to straighten up these two points I would support reinstatement of this contribution by Fernandez.microflown. Dondervogel 2 (talk) 07:37, 5 October 2019 (UTC)[reply]

Thank you very much for your kind review, I've made some changes following your suggestions and left a draft in my user sandbox ( https://en.wikipedia.org/wiki/User:Fernandez.microflown/sandbox ). :Pinging Huon and Dondervogel 2 could you please review the draft to see if this version is suitable? Thank you in advance! Fernandez.microflown (talk) 10:35, 7 October 2019 (UTC)[reply]

The revised draft addresses my main concern, by clarifying that P and V are frequency-domain quantities. It does not address the conversion from acceleration to velocity, but this could be improved once the new contribution is inserted in the article. On this basis, I support inclusion of the revised text, in its present form. Dondervogel 2 (talk) 10:49, 7 October 2019 (UTC)[reply]

I'm no subject-matter expert and would have to do some serious reading to comment on the content. If Dondervogel 2 is OK with it, I'd defer to their judgement. Huon (talk) 21:50, 7 October 2019 (UTC)[reply]

Once again thank you Huon and Dondervogel 2 for your great support and quick reply! I´ve moved the content as discussed. Regarding your question, the moment that a time integral is applied to the gradient it becomes particle velocity, I´ve corrected that in the text. Initially I also included the equation from Jacobsen´s book (p.61, Eq. 6.22), but I thought it was not the best place to add it: ${\hat {v}}_{n}(t)=-\int _{-\infty }^{t}{\frac {p_{2}(\tau )-p_{1}(\tau )}{\rho \Delta r}}d\tau \,.$ Fernandez.microflown (talk) 06:44, 8 October 2019 (UTC)[reply]

References

^ ^a ^b ^c Jacobsen, Finn; de Bree, Hans-Elias (2005-09-01). "A comparison of two different sound intensity measurement principles". The Journal of the Acoustical Society of America. 118 (3): 1510–1517. doi:10.1121/1.1984860. ISSN 0001-4966.
^ Jacobsen, Finn, author. Fundamentals of general linear acoustics. ISBN 9781118346419. OCLC 857650768. {{cite book}}: |last= has generic name (help)CS1 maint: multiple names: authors list (link)
^ FAHY, FRANK. (2017). SOUND INTENSITY. CRC Press. ISBN 1138474193. OCLC 1008875245.

plane wave sound intensity

No source is given and the variables are ambiguous. I suggest an edit similar to my change that was reverted, on the following lines:

For a plane harmonic wave ^[1]

$\mathrm {I} =2\pi ^{2}\nu ^{2}\delta ^{2}\rho c$

$\mathrm {I} =2\pi ^{2}\nu ^{2}\delta ^{2}\rho c=4\pi ^{2}\nu ^{2}\delta _{rms}^{2}\rho c$ Where,

$\nu$ is frequency of sound,

$\delta$ is the peak amplitude of the sound wave particle displacement,

$\delta _{rms}$ is the effective amplitude of the sound wave particle displacement,

$\rho$ is density of medium in which sound is traveling, and

$c$ is speed of sound.

The reason is that a factor 2 is involved if comparing the peak amplitude to the effective amplitude (see https://de.wikipedia.org/wiki/Effektivwert , french and german pages exist, english page seems to be missing). The derivation can be found in Beranek 2012 or 2019 (see source given above). Because the final formula results from the time integration I think the 'Effektivwert' is more approbriate than the peak value. The existing wiki entry is thus in my opinion misleading.

An easier way: $pv=pu\omega =\rho cvu\omega =\rho cu\omega u\omega =\rho c\omega ^{2}u^{2}=4\pi ^{2}f^{2}u^{2}\rho c$ ,

where u is displacement and v is particle velocity and
$v={\frac {\partial u}{\partial t}}$

2A02:21B4:A0E0:1A00:6329:224E:813:3CB (talk) 14:14, 2 October 2023 (UTC) [User:Johnny 17|Johnny 17]] (talk) 14:45, 2 October 2023 (UTC)[reply]

I think it was I who reverted your edit. I did so because I was confused, and I appreciate you responding here. Let us take this one step at a time. You write

\mathrm {I} =2\pi ^{2}\nu ^{2}\delta ^{2}\rho c

where

nu = frequency

rho = density

c = sound speed

and

delta = "peak amplitude".

Assuming that amplitude is the amplitude of a plane wave, what is the difference between the amplitude of that plane wave and the "peak amplitude" of the same plane wave. Dondervogel 2 (talk) 18:26, 2 October 2023 (UTC)[reply]

^ Beranek, Leo L. (2019). Acoustics: Sound Fields, Transducers and Vibration. Second edition. Academic Press. ISBN 978-0-12-815228-7.

[:0-1] Jacobsen, Finn; de Bree, Hans-Elias (2005-09-01). "A comparison of two different sound intensity measurement principles". The Journal of the Acoustical Society of America. 118 (3): 1510–1517. doi:10.1121/1.1984860. ISSN 0001-4966.

[2] Jacobsen, Finn, author. Fundamentals of general linear acoustics. ISBN 9781118346419. OCLC 857650768. {{cite book}}: |last= has generic name (help)CS1 maint: multiple names: authors list (link)

[3] FAHY, FRANK. (2017). SOUND INTENSITY. CRC Press. ISBN 1138474193. OCLC 1008875245.

[4] Beranek, Leo L. (2019). Acoustics: Sound Fields, Transducers and Vibration. Second edition. Academic Press. ISBN 978-0-12-815228-7.

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