1. p, + - [7Q,/(7-1)/(T:)21s: (4,17) the particular parameter values shown in Table
2. Second, Fig. 3 displays two curves of L' as a function of n, while Fig. 4 shows the corresponding w. The solid curves in Figs. 3-4 correspond to lower w, while the dashed ones refer to higher w. Regarding Fig. 3, the region (a) is stable to both frequency modes, the region (b) is stable to lower-w mode but is unstable to higher-w mode, the region (c) is unstable to both modes, and the region (d) is unstable to lower-w mode but is stable to higher-w mode. As seen from Fig. 4, the higher frequencies are approximately 10 times larger than the lower frequencies. If the higher frequencies lie in the acoustic range, only the lower-w modes are considered. In this case, the lower-w curve recovers the classical result^^,^ that the stability is monotonically enhanced with decreasing n. An exact cufoff frequency for nonacoustic L"-instability is meaningless Lo impose unless the cavity acoustics is analyzed. As a consequence, in general cases where both frequencies are assumed to be of interest, the stable regime has to be chosen to be the region (a) of Fig. 3. A system is then most stable at nz 0.63 for this particular case, which contradicts the classical trend of stability increasing with smaller n. A similar stability trend involving a minimum in stability boundary is also obtained with respect to varing values of Et.
3. In Fig. 6 as with Fig. 5, only the larger chamber size is taken from two modes for each case of fixed Qt. The sharp transition in each curve occurs because the solutions for higher-w modes can not be found numerically, for those values of Q, less than a certain value, e.g., Q,=0.3 for Qf-0.8. It is concluded from this figure that a system becomes more stable with higher Q, lower Q, or higher Qf as long as Q. Q, + J,Qf -constant. This fact is true even if only one of the two frequency modes is considered, since both CULVS exhibit negative slopes for a fixed value of Qf. 5. Consideration of the Unsteadv Process