Physically Derived Synthesis Model of a Cavity Tone

Rod Selfridge; Joshua D. Reiss; Eldad J. Avital
DAFx-2017 - Edinburgh
The cavity tone is the sound generated when air flows over the open surface of a cavity and a number of physical conditions are met. Equations obtained from fluid dynamics and aerodynamics research are utilised to produce authentic cavity tones without the need to solve complex computations. Synthesis is performed with a physical model where the geometry of the cavity is used in the sound synthesis calculations. The model operates in real-time making it ideal for integration within a game or virtual reality environment. Evaluation is carried out by comparing the output of our model to previously published experimental, theoretical and computational results. Results show an accurate implementation of theoretical acoustic intensity and sound propagation equations as well as very good frequency predictions. NOMENCLATURE c = speed of sound (m/s) f = frequency (Hz) ω = angular frequency = 2πf (rads/revolution) u = air flow speed (m/s) Re = Reynolds number (dimensionless) St = Strouhal number (dimensionless) r = distance between listener and sound source (m) φ = elevation angle between listener and sound source ϕ = azimuth angle between listener and sound source ρair = mass density of air (kgm−3 ) µair = dynamic viscosity of air (Pa s) M = Mach number, M = u/c (dimensionless) L = length of cavity (m) d = depth of cavity (m) b = width of cavity (m) κ = wave number, κ = ω/c (dimensionless) r = distance between source and listener (m) δ = shear layer thickness (m) δ ∗ = effective shear layer thickness (m) δ0 = shear layer thickness at edge separation (m) θ0 = shear layer momentum thickness at edge separation (m) C2 = pressure coefficient (dimensionless)
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