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A horn is a pointed projection of the skin of various animals. In ruminant artiodactyls, the horns are paired and take various forms depending on the family: Some peoples use bovid horns as musical instruments, for example the shofar. These have evolved into brass instruments in which, unlike the trumpet, the bore gradually increases in width through most of its length - that is to say, it is conical rather than cylindrical. These are called horns, though made of metal. See French horn.
In telecommunication, the term horn has the following meanings:

1. In radio transmission, an open-ended waveguide, of increasing cross-sectional area, which radiates directly in a desired direction or feeds a reflector that forms a desired beam.

Note 1: Horns may have one or more expansion curves, i.e. , longitudinal cross sections, such as elliptical, conical, hyperbolic, or parabolic curves, and not necessarily the same expansion curve in each (E-plane and H-plane) cross section.

Note 2: A very wide range of beam patterns may be formed by controlling horn dimensions and shapes, placement of the reflector, and reflector shape and dimensions.

2. A portion of a waveguide in which the cross section is smoothly increased along the axial direction.

3. In audio systems, a tube, usually having a rectangular transverse cross section and a linearly or exponentially increasing cross-sectional area, used for radiating or receiving acoustic waves.

Source: from Federal Standard 1037C and from MIL-STD-188