Abstract
When a waveguide with a boundary discontinuity is excited by a low‐frequency plane wave, cutoff cross modes are induced by the discontinuity. Although these modes are discernible only in the vicinity of the discontinuity, they act as sources in the incompressible local flow, and thereby affect the mean acoustic pressure. This has a profound effect on the farfield reflection and transmission coefficients R and T, and, consequently, on the junction impedance Z. The method of matched asymptotic expansions shall be used and it will be shown that, by properly accounting for the cross modes, the frequency range of validity of asymptotic estimates of R, T, and Z can be greatly extended. The possibility of improving these estimates by the use of Pade fractions will also be discussed. Finally, the formal difficulties of incorporating cutoff modes into the acoustic field description are discussed, and an extension of the method of matched asymptotic expansions to circumvent them is presented.
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