Acoustic waves in a Rijke tube with radiation impedance

An analysis of acoustic vibrations occurring in a heated gas within a porous cylindrical tube open on one end and closed at the other is presented and extended to the case of a tube traversed cross-sectionally with a heated grating. An expression and boundry conditions are defined for the pressure within the tube and for the acoustic impedance of the gas. Auto-oscillations are demonstrated to occur in the presence of a heated grating in order to dissipate the thermal input. The governing equations for the pressure in the Rijke tube are formulated for a homogeneous system, as are equations for periodic wave numbers which can arise in the tube in the presence of pertubations caused by the heated grill.