Rayl

<h2 id="explanation">Explanation</h2>
<h3>Specific acoustic impedance</h3>
When sound waves pass through any physical substance the pressure of the waves causes the particles of the substance to move. The sound <a href="/facts/Acoustic_impedance/FdXaKVjo">specific impedance</a> is the ratio between the <a href="/facts/Sound_pressure/MgJAcp2I">sound pressure</a> and the <a href="/facts/Particle_velocity/V2SSGkXU">particle velocity</a> it produces.
Specific acoustic impedance is defined as:<a class="footnote-ref" id="fnref:8" href="#fn:8">8</a>

Z
              _
            
          
          (
          
            r
          
          ,
          ω
          )
          =
          
            
              
                
                  
                    p
                    _
                  
                
                (
                
                  r
                
                ,
                ω
                )
              
              
                
                  
                    v
                    _
                  
                
                (
                
                  r
                
                ,
                ω
                )
              
            
          
        
      
    
    {\displaystyle {{\underline {Z}}(\mathbf {r} ,\omega )={\frac {{\underline {p}}(\mathbf {r} ,\omega )}{{\underline {v}}(\mathbf {r} ,\omega )}}}}

where 
 
 
 
 
 
 Z
 _
 
 
 ,
 
 
 p
 _
 
 
 
 
 {\displaystyle {\underline {Z}},{\underline {p}}}
 
 and 
 
 
 
 
 
 v
 _
 
 
 
 
 {\displaystyle {\underline {v}}}
 
 are the specific acoustic impedance, pressure and <a href="/facts/Particle_velocity/V2SSGkXU">particle velocity</a> <a href="/facts/Phasor/LyjSSUDo">phasors</a>, 
 
 
 
 
 r
 
 
 
 {\displaystyle \mathbf {r} }
 
 is the position and 
 
 
 
 ω
 
 
 {\displaystyle \omega }
 
 is the frequency.

<h3>Characteristic acoustic impedance</h3>
The rayl is also used for the characteristic (acoustic) impedance of a medium, which is an inherent property of a medium:<a class="footnote-ref" id="fnref:9" href="#fn:9">9</a>

Z
            
              0
            
          
          =
          
            ρ
            
              0
            
          
          
            c
            
              0
            
          
        
      
    
    {\displaystyle {Z_{0}=\rho _{0}c_{0}}}

Here, 
 
 
 
 
 
 Z
 
 0
 
 
 
 
 
 {\displaystyle {Z_{0}}}
 
 is the characteristic impedance, and 
 
 
 
 
 
 ρ
 
 0
 
 
 
 
 
 {\displaystyle {\rho _{0}}}
 
 and 
 
 
 
 
 
 c
 
 0
 
 
 
 
 
 {\displaystyle {c_{0}}}
 
 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 
 
 
 
 
 
 Z
 _
 
 
 
 
 {\displaystyle {\underline {Z}}}
 
 will be different from the characteristic acoustic impedance 
 
 
 
 
 
 Z
 
 0
 
 
 
 
 
 {\displaystyle {Z_{0}}}
 
.

<h3>MKS and CGS units</h3>
Subscripts are used in this section to distinguish identically named units. Texts often refer to "the MKS rayl" to ensure clarity.
The <a href="/facts/MKS_system_of_units/fMpV1vDw">MKS</a> unit of specific acoustic impedance is the <a href="/facts/Pascal_(unit)/Am1To2Qm">pascal</a>-<a href="/facts/Second/jtFxnJXx">second</a> per <a href="/facts/Meter/hPhzc1CV">meter</a>,<a class="footnote-ref" id="fnref:10" href="#fn:10">10</a> and is often called the rayl (MKS: 1 Rayl = 1 Pa·s·m−1).
The MKS unit and the <a href="/facts/Centimetre%E2%80%93gram%E2%80%93second_system_of_units/qbHxv78q">CGS</a> unit confusingly have the same name, but are not the same quantity (or unit):

<ul><li>As an MKS unit, one rayl equals one <a href="/facts/Pascal_(unit)/Am1To2Qm">pascal</a>-<a href="/facts/Second/jtFxnJXx">second</a> per <a href="/facts/Meter/hPhzc1CV">meter</a> (Pa·s·m−1), or equivalently one <a href="/facts/Newton_(unit)/Ral9XgNl">newton</a>-second per cubic meter (N·s·m−3). Expressed in <a href="/facts/SI_base_unit/M7PsTWg4">SI base units</a>, that is kg·s−1·m−2:<a class="footnote-ref" id="fnref:11" href="#fn:11">11</a>
1 RaylMKS = 1 N⋅s/m3 = 1 Pa⋅s/m = 1 kg/(s⋅m2)</li>
<li>As a CGS unit, one rayl equals one <a href="/facts/Barye/ewnVfHCJ">barye</a>-<a href="/facts/Second/jtFxnJXx">second</a> per <a href="/facts/Centimeter/urPkBdGR">centimeter</a> (ba·s·cm−1), or equivalently one <a href="/facts/Dyne/gHYd2NyK">dyne</a>-second per cubic centimeter (dyn·s·cm−3). Expressed in CGS base units, that is g·s−1·cm−2:
1 RaylCGS = 1 dyn⋅s/cm3 = 1 ba⋅s/cm = 1 g/(s⋅cm2)</li>
<li>The CGS unit rayl is ten times larger than the MKS unit rayl:
1 RaylCGS = 10 RaylMKS</li></ul>

Citations

Sources

<ul><li>Ainslie, M. A. (2010), Principles of Sonar Performance Modeling, Springer</li>
<li>Angelsen, Bjørn (2000). Ultrasound Imaging. Vol. I. Trondheim, Norway: Emantec. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 82-995811-0-9.</li>
<li>Beranek, L. L. (1986), Acoustics, American Institute of Physics</li>
<li>Cobbold, Richard S. C. (2007). Foundations of Biomedical Ultrasound. New York: Oxford University Press. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 978-0-19-516831-0.</li>
<li>Kinsler, L. E.; Frey, A. R. (1962), Fundamentals of Acoustics (2nd ed.), Wiley</li>
<li>Kinsler, L. E.; Frey, A. R.; Coppens, A. B.; Sanders, J. V. (2000), Fundamentals of Acoustics (4th ed.), New York: John Wiley & Sons, Inc.</li>
<li>Morfey, C. L. (2000), Dictionary of acoustics, Academic press</li>
<li>Rossing, T. D. (2007), Springer Handbook of Acoustics, Springer, p. 60</li></ul>

<h2 id="external-links">External links</h2>
<ul><li><a href="https://web.archive.org/web/19990422034128/http://www.unc.edu/%7Erowlett/units/dictR.html">Dictionary of Physics Units of Measurement</a></li>
<li><a href="http://www.sizes.com/units/rayl.htm">A discussion of the history and ambiguity of the rayl</a></li></ul>

<h2 id="references">References</h2>

<ol>
<li id="fn:1">Morfey 2000, pp. 308, 341 - Morfey, C. L. (2000), Dictionary of acoustics, Academic press <a href="#fnref:1" class="footnote-back-ref">↩</a></li>
<li id="fn:2">Kinsler & Frey 1962, p. 122 - Kinsler, L. E.; Frey, A. R. (1962), Fundamentals of Acoustics (2nd ed.), Wiley <a href="#fnref:2" class="footnote-back-ref">↩</a></li>
<li id="fn:3">Beranek 1986, p. 11 - Beranek, L. L. (1986), Acoustics, American Institute of Physics <a href="#fnref:3" class="footnote-back-ref">↩</a></li>
<li id="fn:4">Ainslie 2010, p. 662 - Ainslie, M. A. (2010), Principles of Sonar Performance Modeling, Springer <a href="#fnref:4" class="footnote-back-ref">↩</a></li>
<li id="fn:5">Angelsen 2000, p. 2.8 - Angelsen, Bjørn (2000). Ultrasound Imaging. Vol. I. Trondheim, Norway: Emantec. ISBN 82-995811-0-9. <a href="#fnref:5" class="footnote-back-ref">↩</a></li>
<li id="fn:6">Cobbold 2007, pp. 41–42 - Cobbold, Richard S. C. (2007). Foundations of Biomedical Ultrasound. New York: Oxford University Press. ISBN 978-0-19-516831-0. <a href="#fnref:6" class="footnote-back-ref">↩</a></li>
<li id="fn:7">Kinsler et al. 2000, p. 126 - Kinsler, L. E.; Frey, A. R.; Coppens, A. B.; Sanders, J. V. (2000), Fundamentals of Acoustics (4th ed.), New York: John Wiley & Sons, Inc. <a href="#fnref:7" class="footnote-back-ref">↩</a></li>
<li id="fn:8">Cobbold 2007, pp. 41–42 - Cobbold, Richard S. C. (2007). Foundations of Biomedical Ultrasound. New York: Oxford University Press. ISBN 978-0-19-516831-0. <a href="#fnref:8" class="footnote-back-ref">↩</a></li>
<li id="fn:9">Cobbold 2007, pp. 41–42 - Cobbold, Richard S. C. (2007). Foundations of Biomedical Ultrasound. New York: Oxford University Press. ISBN 978-0-19-516831-0. <a href="#fnref:9" class="footnote-back-ref">↩</a></li>
<li id="fn:10">Kinsler et al. 2000, p. 126 - Kinsler, L. E.; Frey, A. R.; Coppens, A. B.; Sanders, J. V. (2000), Fundamentals of Acoustics (4th ed.), New York: John Wiley & Sons, Inc. <a href="#fnref:10" class="footnote-back-ref">↩</a></li>
<li id="fn:11">Cobbold 2007, pp. 41–42 - Cobbold, Richard S. C. (2007). Foundations of Biomedical Ultrasound. New York: Oxford University Press. ISBN 978-0-19-516831-0. <a href="#fnref:11" class="footnote-back-ref">↩</a></li>
</ol>

Rayl open-in-new

Rayl