Abstract: To investigate the longitudinal acoustic modal frequencies resulting from the geometric parameters of the acoustic cavity, theoretical formulas were developed based on the Rayleigh criterion to calculate the longitudinal acoustic modal frequencies of abrupt area change and dual pulse chambers rapidly. By analyzing the characteristics of the extreme points in the curves of the longitudinal acoustic modal frequencies with respect to the position of the abrupt cross-section or compartment, a method was proposed to determine the upper and lower bounds and verified through acoustic modal experiments under cold flow conditions. The abrupt area change chamber exhibits 2n extreme points along the L₁/L_c curve and intersects the constant cross-section chamber at 2n+1 points, whereas the dual pulse type has 2n-1 extreme points and 2n intersections when L₂/L_c≤1/(2n). The theoretical and experimental results show a relative error of less than 7%, with consistent frequency variation trends. This method enables rapid evaluation and qualitative analysis of the longitudinal acoustic modal frequencies in abrupt area change and dual pulse solid rocket motor chambers, thereby providing a reference for the preliminary design of the chamber.