View source for Rayl

{{Other uses}}
A '''rayl'''{{sfn|ps=|Morfey|2000|pp=308,341}}{{sfn|ps=|Kinsler|Frey|1962|p=122}}{{sfn|ps=|Beranek|1986|p=11}}{{sfn|ps=|Ainslie|2010|p=662}} (symbol '''Rayl'''{{sfn|ps=|Angelsen|2000|p=2.8}}{{sfn|ps=|Cobbold|2007|pp=41–42}}) is one of two units of [[specific acoustic impedance]] and [[characteristic acoustic impedance]]; one an [[MKS system of units|MKS]] unit, and the other a [[Centimetre–gram–second system of units|CGS]] unit. These have the same dimensions as momentum per volume.

The units are named after [[John William Strutt, 3rd Baron Rayleigh]].{{sfn|ps=|Kinsler|Frey|Coppens|Sanders|2000|p=126}} They are not to be confused with the unit of [[photon]] [[flux]], the  [[Rayleigh (unit)|rayleigh]].

== Explanation ==

=== Specific acoustic impedance ===
When sound waves pass through any physical substance the pressure of the waves causes the particles of the substance to move. The sound [[Acoustic impedance|specific impedance]] is the ratio between the [[sound pressure]] and the [[particle velocity]] it produces.

''Specific acoustic impedance'' is defined as:{{sfn|ps=|Cobbold|2007|pp=41–42}}
: <math>{\underline{Z}(\mathbf{r},\omega) = \frac{\underline{p}(\mathbf{r},\omega)}{\underline{v}(\mathbf{r},\omega)}}</math>
where <math>\underline{Z}, \underline{p}</math> and <math>\underline{v}</math> are the specific acoustic impedance, pressure and [[particle velocity]] [[phasor]]s, <math>\mathbf{r}</math> is the position and <math>\omega</math> is the frequency.

=== Characteristic acoustic impedance ===
The rayl is also used for the ''characteristic (acoustic) impedance'' of a medium, which is an inherent property of a medium:{{sfn|ps=|Cobbold|2007|pp=41–42}} 
: <math>{Z_0= \rho_0 c_0}</math>

Here, <math>{Z_0}</math> is the characteristic impedance, and <math>{\rho_0}</math> and <math>{c_0}</math> are the density and speed of sound in the unperturbed medium (i.e. when there are no sound waves travelling in it).

In a viscous medium, there will be a phase difference between the pressure and velocity, so the specific acoustic impedance <math>\underline{Z}</math> will be different from the characteristic acoustic impedance <math>{Z_0}</math>.

=== MKS and CGS units ===
Subscripts are used in this section to distinguish identically named units.  Texts often refer to "the MKS rayl" to ensure clarity.

The [[MKS system of units|MKS]] unit of specific acoustic impedance is the [[pascal (unit)|pascal]]-[[second]] per [[meter]],{{sfn|ps=|Kinsler|Frey|Coppens|Sanders|2000|p=126}} and is often called the rayl (MKS: 1&nbsp;Rayl = 1&nbsp;Pa·s·m<sup>−1</sup>).

The MKS unit and the [[Centimetre–gram–second system of units|CGS]] unit confusingly have the same name, but are not the same quantity (or unit):
* As an MKS unit, one rayl equals one [[pascal (unit)|pascal]]-[[second]] per [[meter]] (Pa·s·m<sup>−1</sup>), or equivalently one [[newton (unit)|newton]]-second per cubic meter (N·s·m<sup>−3</sup>). Expressed in [[SI base unit]]s, that is kg·s<sup>−1</sup>·m<sup>−2</sup>:{{sfn|ps=|Cobbold|2007|pp=41–42}}
*: 1&nbsp;Rayl{{ssub|MKS}} = 1&nbsp;N⋅s/m{{sup|3}} = 1&nbsp;Pa⋅s/m = 1&nbsp;kg/(s⋅m{{sup|2}})
* As a CGS unit, one rayl equals one [[barye]]-[[second]] per [[centimeter]] (ba·s·cm<sup>−1</sup>), or equivalently one [[dyne]]-second per cubic centimeter (dyn·s·cm<sup>−3</sup>). Expressed in CGS base units, that is g·s<sup>−1</sup>·cm<sup>−2</sup>:
*: 1&nbsp;Rayl{{ssub|CGS}} = 1&nbsp;dyn⋅s/cm{{sup|3}} = 1&nbsp;ba⋅s/cm = 1&nbsp;g/(s⋅cm{{sup|2}})
* The CGS unit rayl is ten times larger than the MKS unit rayl:
*: 1&nbsp;Rayl{{ssub|CGS}} = 10&nbsp;Rayl{{ssub|MKS}}

== References ==
; Citations :
{{reflist|30em}}
; Sources :
{{refbegin}}
* {{citation |last1=Ainslie |first1=M. A. |title=Principles of Sonar Performance Modeling |publisher=Springer |year=2010 }}
* {{cite book |last=Angelsen |first=Bjørn |year=2000 |title= Ultrasound Imaging |volume= I |publisher=Emantec |location=Trondheim, Norway |isbn= 82-995811-0-9 }}
* {{citation |last1=Beranek |first1=L. L. |title=Acoustics |publisher=American Institute of Physics |date=1986 }}
* {{cite book |last= Cobbold |first= Richard S. C. |year= 2007 |title= Foundations of Biomedical Ultrasound |publisher= Oxford University Press |location= New York |isbn= 978-0-19-516831-0 }}
* {{citation |last1=Kinsler |first1=L. E. |last2=Frey |first2=A. R. |title=Fundamentals of Acoustics |edition=2nd |publisher=Wiley |date=1962 }}
* {{citation |last1=Kinsler |first1=L. E. |last2=Frey |first2=A. R. |last3=Coppens |first3=A. B. |last4=Sanders |first4=J. V. |date=2000 |title=Fundamentals of Acoustics |edition=4th |publication-place=New York |publisher=John Wiley & Sons, Inc. }}
* {{citation |last1=Morfey |first1=C. L. |date=2000 |title=Dictionary of acoustics |publisher=Academic press }}
* {{citation |last1=Rossing |first1=T. D. |title=Springer Handbook of Acoustics |publisher=Springer |date=2007 |page=60 }}
{{refend}}

== External links ==
* [https://web.archive.org/web/19990422034128/http://www.unc.edu/%7Erowlett/units/dictR.html Dictionary of Physics Units of Measurement]
* [http://www.sizes.com/units/rayl.htm A discussion of the history and ambiguity of the rayl]

[[Category:Units of measurement]]
[[Category:Non-SI metric units]]