# Rayl

A Rayl,[1] rayl or Rayleigh[2] is one of two units of specific acoustic impedance or, equivalently, characteristic acoustic impedance; one an MKS unit, and the other a CGS unit. The units are named after John William Strutt, 3rd Baron Rayleigh, and not to be confused with the rayleigh unit of photon flux, used to measure airglow, and named after his son, Robert John Strutt, 4th Baron Rayleigh. It has the same dimensions as momentum per volume.

## 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 specific impedance is the ratio between the sound pressure and the particle velocity it produces.

Specific acoustic impedance is defined as:[2]

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

where ${\displaystyle {\underline {Z}},{\underline {p}}}$ and ${\displaystyle {\underline {v}}}$ are the specific acoustic impedance, pressure and particle velocity phasors, ${\displaystyle \mathbf {r} }$ is the position and ${\displaystyle \omega }$ 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:[2]

${\displaystyle {Z_{0}=\rho _{0}c_{0}}}$

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

### MKS and CGS units

The MKS unit and the CGS unit confusingly have the same name, but not the same value:

${\displaystyle {\rm {1~Rayl_{MKS}=1~{\frac {N\cdot s}{m^{3}}}=1~{\frac {Pa\cdot s}{m}}=1~{\frac {kg}{s\cdot m^{2}}}}}}$
• In CGS units, 1 Rayl equals 1 barye-second per centimeter (ba·s·cm−1), or equivalently 1 dyne-second per cubic centimeter (dyn·s·cm−3). In CGS base units, that is g∙s−1∙cm−2.
${\displaystyle {\rm {1~Rayl_{CGS}=1~{\frac {dyn\cdot s}{cm^{3}}}=1~{\frac {ba\cdot s}{cm}}=1~{\frac {g}{s\cdot cm^{2}}}}}}$
• 1 CGS Rayl = 10 MKS Rayl. In other words, a CGS Rayl is ten times larger than an MKS Rayl due to the way they are defined.

## References

1. ^ Angelsen, Bjørn (2000). Ultrasound Imaging. I. Trondheim, Norway: Emantec. p. 2.8. ISBN 82-995811-0-9.
2. ^ a b c d Cobbold, Richard S. C. (2007). Foundations of Biomedical Ultrasound. New York: Oxford University Press. pp. 41–42. ISBN 978-0-19-516831-0.

T. D. Rossing, Springer Handbook of Acoustics, Springer, 2007, p. 60

L. E. Kinsler, A. R. Frey, A. B. Coppens, and J. V. Sanders, Fundamentals of Acoustics, Fourth Edition (New York: John Wiley & Sons, Inc.,2000), p. 126