The propagation of a sound pulse in the presence of a semi-infinite open-ended channel. I

Abstract

The behaviour of a sound pulse approaching and progressing beyond the open end of a semi­ infinite channel is discussed. A succession of diffracted waves is created at the open end for which a general formula is obtained, by operational methods, when the pulse originates inside the channel. With the aid of a simple reciprocity relation the asymptotic behaviour of these diffracted waves can be used to deduce the form of the wave returning along the channel when the original pulse approaches the open end from an arbitrary direction. Ultimately the returning wave becomes sensibly plane and separates into regions of length equal to the width of the channel, the form of the potential depending on the number of diffracted waves which contribute to each particular region. Explicit expressions are obtained for the potential in the first two regions at the head of the returning wave and for the third region when the pulse originates inside the channel. The case of an initial velocity distribution given by the Heaviside unit pulse is treated in detail.