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 t ...

, 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 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 hea ...

. 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 ratio of a substance's mass to its volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' (or ''d'') can also be u ...

, *

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 elasticity (solid mechanics), elastic medium. More simply, the speed of sound is how fast vibrations travel. At , the speed of sound in a ...

, *

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 The Mach number (M or Ma), often only Mach, (; ) 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 Austrian physicist and philosopher Erns ...

is small,

M<1

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

References

{{reflist, 30em Fluid dynamics Acoustics