Reply to "Comment on 'Linear and nonlinear frequency shifts in acoustical resonators with varying cross sections' [J. Acoust. Soc. Am. 110, 109-119 (2001)]" (L)

M. P. Mortell and B. R. Seymour [M. P. Mortell and B. R. Seymour [J. Acoust. Soc. Am. 124, 3381-3385 (2008)] offer commentary on the analysis and the conclusions reached in a paper by Hamilton et al. [M. F. Hamilton, Yu. A. Ilinskii, and E. A. Zabolotskaya, J. Acoust. Soc. Am. 110, 109-119 (2000)] on linear and nonlinear frequency shifts in acoustical resonators that are close to cylindrical in shape. The present reply demonstrates that the criticisms made in the Comment are unwarranted when placed in context of the stated restrictions on the theory and the applications for which the theory is intended. It is also shown that the strongest criticisms made in the Comment stem from a mathematical error they introduced when attempting to reproduce the results of Hamilton et al. (C) 2008 Acoustical Society of America. [DOI: 10.1121/1.3003934]