aeroacoustics Aeroacoustics is a branch of acoustics that studies noise generation via either turbulent fluid motion or aerodynamic forces interacting with surfaces. Noise generation can also be associated with periodically varying flows. A notable example of th ...

, Lighthill's eighth power law states that power of the sound created by a turbulent motion, far from the turbulence, is proportional to eighth power of the characteristic turbulent velocity, derived by

Sir James Lighthill Sir Michael James Lighthill (23 January 1924 – 17 July 1998) was a British applied mathematician, known for his pioneering work in the field of aeroacoustics and for writing the Lighthill report on artificial intelligence. Biography J ...

in 1952.Lighthill, M. J. (1954, February). On sound generated aerodynamically. II. Turbulence as a source of sound. In Proc. R. Soc. Lond. A (Vol. 222, No. 1148, pp. 1–32). This is used to calculate the total acoustic power of the

jet noise In aeroacoustics, jet noise is the field that focuses on the noise generation caused by high-velocity jets and the turbulent eddies generated by shearing flow. Such noise is known as broadband noise and extends well beyond the range of human heari ...

. The law reads as :

W = K \frac L^2 U^8,

where *

W

is the acoustic power in the far-field, *

K

is the proportionality constant (or Lighthill's constant), *

\rho_o

is the uniform fluid

density Density (volumetric mass density or specific mass) is the substance's mass per unit of volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' can also be used. Mathematical ...

, *

c_o

is the

speed of sound The speed of sound is the distance travelled per unit of time by a sound wave as it propagates through an elastic medium. At , the speed of sound in air is about , or one kilometre in or one mile in . It depends strongly on temperature as w ...

, *

L

is the characteristic length scale of the turbulent source and *

U

is the characteristic velocity scale of the turbulent source. The eighth power is experimentally verified and found to be accurate for low speed flows, i.e.,

Mach number Mach number (M or Ma) (; ) is a dimensionless quantity in fluid dynamics representing the ratio of flow velocity past a boundary to the local speed of sound. It is named after the Moravian physicist and philosopher Ernst Mach. : \mathrm = \frac ...

is small,

M<1

. And also, the source has to be compact to apply this law.

References

{{reflist, 30em Fluid dynamics Acoustics