Table 1 Parameters related to conversion... | Emerald Publishing

Table 1

Parameters related to conversion between rotary acoustic cavities

Cavity type	Related parameter
Cavity type	Parameter type	Specific parameter
Conical acoustic cavity	Coordinate relation	$α_{1} = η_{1}$ ⁠, $β_{1} = θ_{1}$ $z_{1} = ξ_{1}$
	Transformation	$\| J_{1} \| = L_{1} H \cos α$ ⁠, $J_{11}^{1} = 1 / H$ ⁠, $J_{21}^{1} = \tan α / H$ ⁠, $J_{12}^{1} = 0$ ⁠, $J_{22}^{1} = 1 / L_{1} \cdot \cos α$
	Lame coefficient	$H_{α_{1}} = 1$ ⁠, $H_{β_{1}} = r_{1} = R_{2} + (R_{1} - R_{2}) \cdot η + H \cdot ξ$ ⁠, $H_{z_{1}} = 1$
	Value range	$0 \leq L_{α_{1}} \leq 1$ ⁠, $0 \leq L_{β_{1}} \leq ϑ_{1}$ ⁠, $0 \leq L_{z_{1}} \leq 1$
Cylindrical acoustic cavity	Coordinate relation	$α_{2} = s_{2}$ ⁠, $β_{2} = θ_{2}$ ⁠, $z_{2} = r_{2}$
	Transformation	$\| J_{2} \| = 1$ ⁠, $J_{11}^{2} = J_{22}^{2} = \sqrt{2} / 2$ ⁠, $J_{12}^{2} = J_{21}^{2} = 0$
	Lame coefficient	$H_{α_{2}} = 1$ ⁠, $H_{β_{2}} = r_{2}$ ⁠, $H_{z_{2}} = 1$
	Value range	$0 \leq L_{α_{2}} \leq L_{2}$ ⁠, $0 \leq L_{β_{2}} \leq ϑ_{2}$ ⁠, $0 \leq L_{z_{2}} \leq H$

Cavity type	Related parameter
Cavity type	Parameter type	Specific parameter
Conical acoustic cavity	Coordinate relation	$α_{1} = η_{1}$ , $β_{1} = θ_{1}$ $z_{1} = ξ_{1}$
	Transformation	$\| J_{1} \| = L_{1} H \cos α$ , $J_{11}^{1} = 1 / H$ , $J_{21}^{1} = \tan α / H$ , $J_{12}^{1} = 0$ , $J_{22}^{1} = 1 / L_{1} \cdot \cos α$
	Lame coefficient	$H_{α_{1}} = 1$ , $H_{β_{1}} = r_{1} = R_{2} + (R_{1} - R_{2}) \cdot η + H \cdot ξ$ , $H_{z_{1}} = 1$
	Value range	$0 \leq L_{α_{1}} \leq 1$ , $0 \leq L_{β_{1}} \leq ϑ_{1}$ , $0 \leq L_{z_{1}} \leq 1$
Cylindrical acoustic cavity	Coordinate relation	$α_{2} = s_{2}$ , $β_{2} = θ_{2}$ , $z_{2} = r_{2}$
	Transformation	$\| J_{2} \| = 1$ , $J_{11}^{2} = J_{22}^{2} = \sqrt{2} / 2$ , $J_{12}^{2} = J_{21}^{2} = 0$
	Lame coefficient	$H_{α_{2}} = 1$ , $H_{β_{2}} = r_{2}$ , $H_{z_{2}} = 1$
	Value range	$0 \leq L_{α_{2}} \leq L_{2}$ , $0 \leq L_{β_{2}} \leq ϑ_{2}$ , $0 \leq L_{z_{2}} \leq H$