Acoustical horn
View Patent ↗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.
1. 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.
2. A horn according to claim 1 , wherein d =1 and ζ tends to 1, and the cross-section of the portion is substantially rectangular.
3. A horn according to claim 1 , wherein ζ=0 and the cross-section of the portion is elliptical.
4. A horn according to claim 3 , wherein y 2 +z 2 =R 2 and the cross-section is circular and defined by;
R ( x ) = R 0 ( a·e mx − b·e −mx )
where R 0 is the radius of the portion at the upstream end thereof.
5. A horn according to claim 1 , wherein d =f(x) and the cross-section of the portion morphs from a first shape, preferably circular, at the upstream end of the portion to another shape at the downstream end.
6. A horn according to claim 5 , wherein d =x/L where L is the length of the portion from the upstream to the downstream end thereof.
7. A horn according to claim 1 wherein 2 <a <3.
8. A horn according to claim 1 wherein 1 <b <2.
9. A horn according to claim 1 , having been sculpted from a block of material.
10. A horn according to claim 9 , wherein the material is medium density fibre board (MDF).
11. A horn according to claim 9 , wherein the block is made up of a plurality of layers joined together one upon another.
12. A loudspeaker comprising a horn according to claim 1 , and means for delivering acoustic energy to the throat thereof.
13. A loudspeaker according to claim 12 , wherein the means for delivering acoustic energy comprises at least two energy sources optimized for different frequency ranges.
14. A loudspeaker according to claim 12 , wherein the means for delivering acoustic energy comprises at least one compression driver.
15. A loudspeaker according to claim 14 , wherein the driver is a dual concentric compression driver.