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The Quarterly Journal of Mechanics and Applied Mathematics 1953 6(3):313-335; doi:10.1093/qjmam/6.3.313
© 1953 by Oxford University Press
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THE TRANSIENT MOTION OF SOUND WAVES IN TUBES

J. D. PEARSON

( Department of Mathematics, The University Manchester )

This paper falls into two parts; sections 2–5 deal with the transient motion of sound waves in an infinite tube of constant cross-section; while in sections 6–9 the effect of slight distortion of the cross-section is considered. In the first PARTa formula is obtained for the velocity potential by use of Heaviside's operators, and an asymptotic expression for this is then found by the method of steepest descent. In the second PARTof the paper a series solution is obtained for the velocity potential in a tube of slightly variable cross-section. The particular case of a tube of near rectangular cross-section is investigated, and for such a tube a longitudinal harmonic distortion is considered in detail.


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