Solution Characteristics of the Retarded-Time Equation for Transonic Rotating Sources
Nomenclature c0 = speed of sound in undisturbed media, m∕s f0 = self-frequency of monopole source, Hz M = Mach number Mcr = critical Mach number Mr = Mach number of moving source in radiation direction n = quotient Δ t; 2π R τ = jx − yj, distance between observer and source, m R τ = nondimensional distance between observer and source r = radial coordinate, m r = rx∕ry, nondimensional radial coordinate t = observer time, s t = jωjt, nondimensional observer time trel = t − tmin, relative observer time x = observer position vector, m y = source position vector, m z = axial coordinate, m z = zx − zy ∕ry, nondimensional axial coordinate Δ t = tmax − tmin, observer time difference between two successive local extremes Δ tm = mod Δ t; 2π Δθ = sgn ω θy − θx , azimuthal angle between observer and source, rad θ = azimuthal angle, rad τ = source time, s τ = jωjτ, nondimensional source time ω = angular speed of source, rad∕s