# Lighthill's eighth power law

In aeroacoustics, 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[1][2]. This is used to calculate the total acoustic power of the jet noise. The law reads as

${\displaystyle W=K{\frac {\rho _{o}}{c_{o}^{5}}}L^{2}U^{8},}$

where

• ${\displaystyle W}$ is the acoustic power in the far-field,
• ${\displaystyle K}$ is the proportionality constant (or Lighthill's constant),
• ${\displaystyle \rho _{o}}$ is the uniform fluid density,
• ${\displaystyle c_{o}}$ is the speed of sound,
• ${\displaystyle L}$ is the characteristic length scale of the turbulent source and
• ${\displaystyle U}$ 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 is small, ${\displaystyle M<1}$. And also, the source has to be compact to apply this law.

## References

1. ^ Lighthill, M. J. (1952, March). On sound generated aerodynamically I. General theory. In Proc. R. Soc. Lond. A (Vol. 211, No. 1107, pp. 564–587). The Royal Society.
2. ^ 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).