Line integral theory of barrier attenuation in the presence of the ground

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Abstract
A theory of diffraction is presented that is based on the line integral along the free edge of a semi‐infinite barrier. Expressions, which are not integrable analytically, are given for the cases where the source/receiver line is and is not perpendicular to the edge of the barrier. In this latter case the ’’offset’’ between source and receiver along the barrier enters into the mathematical expression in a more complicated way than hitherto supposed. When the barrier is situated on ground of finite impedance, the amplitude of the sound field is no longer expressible as a single constant that can be taken outside the integrand, but becomes a more complicated function than when the barrier is in free space and involves other parameters such as the source, receiver and barrier heights, and the impedance of the ground. These expressions are suitable for calculating (by numerical integration) the sound field behind a barrier due to the combined effects of direct, reflected, and ground waves in the practical situations where source and receiver are within a few meters of the ground and each several meters from the barrier.

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