Dynamic response of a transducer mounted at one end of an acoustical cavity which is subjected to a specified pressure at the open end of the cavity

The purpose of this report is to develop a mathematical model for a pressure transducer mounted in a fluid filled cavity (a system) and examine the pressure 'measurement' error of the cavity and transducer by computing the dynamic response (output pressure) of the system to a specified pressure time history (input pressure). The 'measurement' error is determined by comparing the calculated output pressure to the specified input pressure. The dynamic response of a transducer mounted at one end of a one-dimensional acoustical cavity is determined. The cavity is filled with a compressible isentropic fluid, and the fluid at the open end of the cavity (i.e., the boundary at x = 0) is subjected to a specified uniform axial input pressure. At the other end of the cavity the transducer is represented as a mass, spring, and damper system. Consequently, the boundary condition at x = (ell) is also time dependent. The general solution to the boundary value problem, as well as the steady state solution for periodic excitation, is obtained by integrating a coupled set of ordinary differential equations.