Patent ID: 8213658

Claim:
An acoustical horn having an inlet or throat, and an outlet or mouth, wherein the shape of at least a portion of the horn between the throat and the mouth is defined by an exponential function including a negative exponential term, wherein in said portion the cross-sectional dimensions of the horn orthogonal to an axis of propagation of the horn increase with distance along the axis of propagation in accordance with the following relationships: y ( x,θ )= y 0 ·( a·e mx −b·e −mx ) cos θ (1−ζd) z ( x,θ )= z 0 ·( a′·e m′x −b′·e −m′x ) sin θ (1−ζd) where x is the distance along the axis of propagation from the upstream end of the section; y, z are the cross-sectional dimensions of the horn orthogonally to x and to each other; v 0 , z 0 are the cross-sectional dimensions at the upstream end of the section (x=0); θ is the polar angle about the axis of propagation (0 <θ<π/2) a, a′, b′ and b are positive constants, preferably a, a′>1 and b, b′>0; m,m′=2πf c/ c and 2πf′ c/ c respectively where f c and f′ c are cut-off frequencies of the horn determined by the y and z dimensions respectively and c is the velocity of sound in air; ζ is a parameter, 0 <ζ<1; and d is either unity or a function of x such that d increases from 0 at the upstream end of the portion to 1 at the downstream end of the portion.