Diffraction of a spherical wave by a hard half-plane: Approximation of the edge field in the frequency domain

The diffraction of a spherical sound wave by a thin hard half-plane is considered. The total field at any position in the space surrounding the edge of the half-plane is composed of three components, two of which are expressed from pure geometrical considerations, and a third component which seems to originate from fictive sound sources situated on the edge of the half plane. This paper takes the expression of the edge-diffracted field as formulated in the Biot-Tolstoy theory of diffraction for the case of a doublet sound signal emanating from the sound source [Biot and Tolstoy (1957). J. Acoust. Soc. Am. 29, 381-391] but rearranged later in a more tractable form by Medwin [(1981). J. Acoust. Soc. Am. 69, 1060-1064] for the more general case of a Dirac-like pulse. Hence a development in the frequency domain of the Fourier transform of the exact expression of the edge-diffracted field in the time domain takes into consideration a part with known special mathematical functions, and a part containing a serial development. This latter also expressed in some special mathematical functions, converges quite rapidly to the numerical Fourier transform of the exact time-domain expression. The presented solution may be used as a good approximation in simulations and in real case predictions of sound attenuation by thin hard barriers.