Acoustical Klein-Gordon equation: a time-independent perturbation analysis.
The perturbation analysis of an ideal acoustical duct was first made by Rayleigh in 1878 and the result has since stood in the literature. However, the analysis is based on the assumption of potential and kinetic energy densities that remain constant as a change in cross section occurs, whereas, in fact, they may fluctuate significantly in comparison to the slowly varying "wave function," Psi(x,t), of the acoustical Klein-Gordon equation. The square of the time-independent eigenfunction, psi(2)(x), is directly proportional to the potential energy per unit length of fluid, and it is shown that it is precisely the perturbation in potential energy that defines correctly the eigenvalue shifts.
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Barbara J
BJ
Forbes
E Roy
ER
Pike