Scattering of a spherical wave by a thin hard barrier on a reflecting plane

This paper is concerned with studying the problem of scattering of a spherical wave by a thin hard barrier on a hard plane. This problem is relevant to investigating the effect on the early part of the sound field of a large room, when a simple, thin and hard strip-like element is set horizontally on a side wall. This scattering element may be a sound reinforcing reflector or an idealisation of a side balcony. Three different calculation models based on ray acoustic concepts and on solutions to the problem of diffraction by a half plane are dealt with and compared to each other. For the case of the half plane, one of the models, the Biot–Tolstoy theory of diffraction, is a treatment in the time domain whereas the two other ones are approximate and give solutions in the frequency domain (one of them is the Geometrical Theory of Diffraction). The expression of the diffracted field in the time domain approach is exact but quite complicated so that, it has not been possible to give its Fourier transform in an exact form. In an earlier publication on this subject, the problem is overcome by making a simple analytical approximation of the early part the diffracted field, and then, adding to its exact Fourier transform the Digital Fourier Transform of the remaining part of the diffracted field. In this paper, an improvement is given to the expression of this early part of the diffracted field and it is shown that for both the time and the frequency domains, this new form is accurate enough for most engineering purposes. Moreover, the frequency form of this latter has a very simple expression. As one is interested in covering as large a low frequency range as possible, multiple diffraction is also implemented in each model to take into account the finite width of the barrier on the plane. Some experimental results are presented also supporting the theoretical predictions quite favourably.