Abstract
The acoustic characteristics of a cylindrical tube of radius ρ0, fitted with a conical flange, of semi-angle O0, are investigated. Let the acoustic potential in the tube be given by O = Ae−ik(x−α) − A′eik(x−α). In this expression the first term represents an incident wave travelling along the tube in the direction of increasing x towards the open end x = 0 and the second term represents the reflected wave. It is shown that, apart from the introduction of the phase shift α = 1/4ρ0 sin O0, the acoustic impedance of the tube is given, to a good approximation, by (A − A′)/(A + A′) = (ikρ0 cos2½O0)/(ikρ0 + sin O0), provided O0 is moderately small. The result is a generalization of a previous investigation [1, Chester 1983]. The earlier restriction to long waves is relaxed in the present work.
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