Use of symbolic manipulation in physical acoustics.

The development of a mathematical theory in acoustics (or in any other field) depends on the insight of the theoretician. However, the formulation of an insight into an equation derived from first principles involves much time spent in activities that fall within the category of a symbolic manipulation. To demonstrate the role symbolic manipulation software can play in the solution process, classical problems in acoustics will be selected. It is known that the solution to the linearized governing equations of an acoustic field can be considered as a superposition of vorticity, thermal, and acoustic modes. However, these modes are coupled. The separation of these modes will be demonstrated. Symbolic manipulation will be used to explore how the higher-order terms in the perturbation parameters, εμ, and εκ, affect the modal coupling. The issue of asymptotic degeneracy will also be addressed (the effects of varying the rates at which these parameters approach zero). [ABSTRACT FROM AUTHOR]