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30 60 SPHERICAL 60 SPHERICAL ANGLE acoustic analogy aerodynamic noise amplitude pressure wave analysis ANGLE FROM EXHAUST Applied to Shock body forces cgs units Comparison of Spectra Computed by Model constant intensity coordinates curvilinear coordinate density dependent variables derivation differential equation Directionality Field Distance from Shock entropy changes entropy effects entropy function entropy production entropy variations entropy-producing regions Equation 3.2 EXHAUST AXIS DEG Experimentally by Smith faGl Figure finite amplitude pressure following form forcing function function of entropy governing equation isentropic process J-wave J=Constant Process Applied Layer Transition Flow Lines of Constant Mach disc moderate shock waves non-isentropic propagation speed non-isentropic region North American Aviation Parabaloidal Shock parameter perturbed region plug nozzle Polar Graphs propagation characteristics quiescent region represented Shock Layer Transition SHOCK RADIUS shock transition Smith Program Firing Spectra Computed SPHERICAL ANGLE DEGREES supersonic nozzle tends to zero thermodynamic process thermodynamic variables upstream Mach number velocity fluctuations weak shocks