Exact solution for one-dimensional acoustic fields in ducts with a quadratic mean temperature profile

Manoj Kumar, B. ; Sujith, R. I. (1997) Exact solution for one-dimensional acoustic fields in ducts with a quadratic mean temperature profile Journal of the Acoustical Society of America, 101 (6). pp. 3798-3799. ISSN 0001-4966

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Official URL: http://asa.scitation.org/doi/abs/10.1121/1.418385

Related URL: http://dx.doi.org/10.1121/1.418385

Abstract

The purpose of this Letter is to present an exact analytical solution for sound propagation in ducts with a quadratic mean temperature profile. Using appropriate transformations, the one-dimensional wave equation for ducts with an axial mean temperature gradient was reduced to the hypergeometric differential equation, whose solution can be expressed in terms of hypergeometric functions. The analysis neglects the effects of mean flow and is therefore valid only for small mean Mach numbers.

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