Arayl^[1][2][3][4] (symbolRayl^[5][6]) is one of two units ofspecific acoustic impedance andcharacteristic acoustic impedance; one anMKS unit, and the other aCGS unit. These have the same dimensions as momentum per volume.

The units are named afterJohn William Strutt, 3rd Baron Rayleigh.^[7] They are not to be confused with the unit ofphotonflux, therayleigh.

When sound waves pass through any physical substance the pressure of the waves causes the particles of the substance to move. The soundspecific impedance is the ratio between thesound pressure and theparticle velocity it produces.

Specific acoustic impedance is defined as:^[6]

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

where${\displaystyle \underset{\_}{Z},\underset{\_}{p}}$ and${\displaystyle \underset{\_}{v}}$ are the specific acoustic impedance, pressure andparticle velocityphasors,${\displaystyle \mathbf{r}}$ is the position and${\displaystyle \omega }$ is the frequency.

The rayl is also used for thecharacteristic (acoustic) impedance of a medium, which is an inherent property of a medium:^[6]

${\displaystyle Z_0={\rho }_0{c}_0}$

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${\displaystyle \underset{\_}{Z}}$ will be different from the characteristic acoustic impedance${\displaystyle Z_0}$.

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

TheMKS unit of specific acoustic impedance is thepascal-second permeter,^[7] and is often called the rayl (MKS: 1 Rayl = 1 Pa·s·m⁻¹).

The MKS unit and theCGS unit confusingly have the same name, but are not the same quantity (or unit):

• As an MKS unit, one rayl equals onepascal-second permeter (Pa·s·m⁻¹), or equivalently onenewton-second per cubic meter (N·s·m⁻³). Expressed inSI base units, that is kg·s⁻¹·m⁻²:^[6]

  1 Rayl_MKS = 1 N⋅s/m³ = 1 Pa⋅s/m = 1 kg/(s⋅m²)

• As a CGS unit, one rayl equals onebarye-second percentimeter (ba·s·cm⁻¹), or equivalently onedyne-second per cubic centimeter (dyn·s·cm⁻³). Expressed in CGS base units, that is g·s⁻¹·cm⁻²:

  1 Rayl_CGS = 1 dyn⋅s/cm³ = 1 ba⋅s/cm = 1 g/(s⋅cm²)

• The CGS unit rayl is ten times larger than the MKS unit rayl:

  1 Rayl_CGS = 10 Rayl_MKS

Citations

Sources

• Dictionary of Physics Units of Measurement
• A discussion of the history and ambiguity of the rayl

• Units of measurement
• Non-SI metric units