Exact Error Bounds for the Phase Velocity in an Acoustic Wave Guide
Abstract
The dispersion curve for waves propagating in an infinite homogeneous isotropic elastic cylinder with finite cross section is studied. A wave f(x,y)exp i(omega t  beta z) is found by collocation or a similar least squares boundary fitting technique that very nearly satisfies the condition that the stress at the boundary be zero. It is proved that for fixed beta there exist an omega' close to omega and a nontrivial function g such that g(x,y)exp i(omega' t  beta z) is a solution and the stress is zero at every point of the boundary. The distance between omega and omega' is bounded by a function of the stress generated by the original wave and the cross section of the cylinder. Thus a window with slope 1/beta is obtained through which the dispersion curve must pass. Rigorous bounds on the width of the window are obtained.
 Publication:

SIAM Journal on Numerical Analysis
 Pub Date:
 August 1978
 DOI:
 10.1137/0715048
 Bibcode:
 1978SJNA...15..715H
 Keywords:

 Acoustic Ducts;
 Acoustic Propagation;
 Elastic Cylinders;
 Error Analysis;
 Phase Velocity;
 Curve Fitting;
 Extremum Values;
 Isotropic Media;
 Least Squares Method;
 Propagation Modes;
 Wave Dispersion;
 Waveguides;
 Acoustics