# Physics:Lighthill's eighth power law

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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

- [math]\displaystyle{ W = K \frac{\rho_o}{c_o^5} L^2 U^8, }[/math]

where

- [math]\displaystyle{ W }[/math] is the acoustic power in the far-field,
- [math]\displaystyle{ K }[/math] is the proportionality constant (or Lighthill's constant),
- [math]\displaystyle{ \rho_o }[/math] is the uniform fluid density,
- [math]\displaystyle{ c_o }[/math] is the speed of sound,
- [math]\displaystyle{ L }[/math] is the characteristic length scale of the turbulent source and
- [math]\displaystyle{ U }[/math] 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, [math]\displaystyle{ M\lt 1 }[/math]. And also, the source has to be compact to apply this law.

## References

- ↑ 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.
- ↑ 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).

Original source: https://en.wikipedia.org/wiki/ Lighthill's eighth power law.
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