Vibroacoustic Simulation. Alexander Peiffer

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StartFraction upper A Subscript ref Baseline Over 4 pi r squared EndFraction right-brace EndLayout"/>

      yields

       StartLayout 1st Row 1st Column upper L Subscript p 2nd Column equals upper L Subscript w Baseline plus 10 log Subscript 10 Baseline left-brace StartFraction upper A Subscript ref Baseline Over 4 pi r squared EndFraction right-brace with normal upper Pi prime Subscript ref Baseline equals StartFraction upper A Subscript ref Baseline p Subscript ref Superscript 2 Baseline Over rho 0 c 0 EndFraction period EndLayout (2.171)

normal upper Pi prime Subscript ref Baseline almost-equals 10 Superscript negative 12 Baseline normal upper W equals normal upper Pi Subscript ref

      matching well to the reference value of acoustic power.

      Bibliography

      1 W.R. Graham. BOUNDARY LAYER INDUCED NOISE IN AIRCRAFT, PART I: THE FLAT PLATE MODEL. Journal of Sound and Vibration, 192(1): 101–120, April 1996. ISSN 0022-460X.

      2 Finn Jacobsen. PROPAGATION OF SOUND WAVES IN DUCTS. Technical Note 31260, Technical University of Denmark, Lynby, Denmark, September 2011.

      3 Reinhard Lerch and H. Landes. Grundlagen der Technischen Akustik, September 2012.

      4 P.M.C. Morse and K.U. Ingard Theoretical Acoustics. International Series in Pure and Applied Physics. Princeton University Press, 1968. ISBN 978-0-691-02401-1.

      Notes

      1 1 Keeping v0≠0 would lead to the convective wave equation that is used in the context of flow related acoustic problems, which is more a topic of aero acoustics

      2 2 Negative k means propagation in positive x-direction, because of the jωt convention. This is the reason why pure acoustic textbooks usually take the −jωt convention in order to get positive wavenumber for positive propagation.

      3 3 This can be proven using the relationship between the δ and exponential functions

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