Approximate computation of acoustic reflection and shadow effects using the Kirchhoff method

Open Access

Table 1

Cases “Reflection side”, “Shadow side”, “Outgoing wave” and values of the coefficients κ₁ and κ₂ depending on the case.

	(a)	(b)	(c)	(d)
Case:	Reflection side	Shadow side	Outgoing wave (1)	Outgoing wave (2)
$(\vec{x} - \vec{y}) \cdot \vec{n}$ $(\vec{x}-\vec{y})\cdot \vec{n}$	>0	<0	>0	<0
$(\partial p_{inc} / \partial n) (\partial p_{inc} / \partial τ)$ $\left(\partial {p}_{{inc}}/{\partial n}\right)\left(\partial {p}_{{inc}}/{\partial \tau }\right)$	>0	>0	<0	<0

Values of κ₁ and κ₂	κ₁ = 1	κ₁ = 1	κ₁ = 0	κ₁ = 0
	κ₂ = 1	κ₂ = 0

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