horn beaming

It depends what you mean by beaming. The generally accepted definition usually refers to a horn whose directivity increases as the frequency rises. If you mean why don’t horns radiate omni-directionally it is because the walls of the horn constrain the sound to a smaller angle. This is usually a desirable thing but it is possible to design a horn that radiated omni-directionally if required.

So why do horns confine the radiation pattern? Because they have solid walls that stop sound waves passing through (yes I know there will be a little transmission).  The sound waves therefore have to radiate at an angle dictated by the horn shape.

At low frequencies the horn loses control over the radiation pattern. This is due to diffraction. The mouth of the horn can be considered an opening through which sound passes. Where the opening is small compared to the wavelength the radiated sound is spherical. The following diagram illustrates what happens.

When the horn becomes large relative to the wavelengths most of the sound just keeps going at the angle of the horn.

Exponential horns and others with curved walls have a radiation pattern that narrows as the frequency increases. The best way to explain this without the use of maths is to start from what we said above; that the sound is constrained by the walls of the horn. If you flip that the other way round then if the sound can’t feel the horn wall it has no control over the radiation pattern. If you now imagine the sound wave as a bubble whose diameter expands until it is equal to one wavelength of the frequency. If the dimension across the horn is greater than that dimension the bubble loses contact with the wall. Lower frequencies see more of the horn and radiate at the angle set near the mouth whereas higher frequencies only see the section close to the throat where the wall angle is less.

At very high frequencies, where the throat dimension is comparable with the wavelengths involved, the horn becomes largely irrelevant.