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A horn generally has excellent efficiency. It can be as much as ten times higher than that of a conventional loudspeaker. If a flare is positioned in front of a diaphragm, the loudspeaker is able to propagate its energy far more efficiently into the surrounding air.
Since the cross-sectional area inside the horn increases with length, the area of the effective radiating surface is increased. In effect we are shifting the radiation resistance of the throat (thin end of the horn) to make it the radiation resistance of the mouth (opening of the horn).
Horn speakers are not only available with tapered cross sections, there is an infinite number of shapes and lengths and they all have their own directivity characteristics. The increase in the surface area inside the horn is also referred to as growth.

In an exponential horn, the cylindrical cross-section A increases exponentially with distance x. Ax = Ah * e ^ ( k * x) Ax = cylindrical cross-section at that distance x Ah = throat area k = flare constant which determines how much the horn opens up along length x.

When you design a horn, you have several criteria:

• What frequency response you desire
• What driver you will use (and its parameters)
• How much compromise you are willing to accept (size, shape, materials, etc.)

The driver and frequency response determine the type and size of the ideal horn, and for a bass horn the maximum size will affect the output and probably the design criteria.

Note that many existing horn designs (and this is especially true for bass horns) often have massive compromises or deviations from what might be an ideal horn. Many Lowther rear-loaded bass horns have been designed by large amounts of experimentation to achieve the best sound given the compromises (often size) that are imposed. Beware when designing your own horn that you understand why things were designed a certain way. This is especially true if you are using or building on current designs.

The first thing to calculate is the throat area. This is determined by the driver parameters. There might be existing well-know throat sizes for certain drivers. Lowther drivers are often used in rear-loaded horns with throats ranging from about 50 cm2 to 150 cm2.

This is tied to mouth area. If the mouth area is too large, or the horn length is too long, you might want to shorten the horn. This is a compromise. To reduce the size of a bass horn, you can either shorten the horn or increase the flare cutoff frequency. If you increase the flare frequency, you can still build a horn with "ideal" properties, but it will only play down to the flare cutoff frequency, then drop like a stone at lower frequencies. If you keep the flare frequency but shorten the horn (also reducing mouth size), you keep the lower frequencies somewhat, but you get impedance peaks below the ideal mouth size. These peaks create a bumpy frequency response below the mouth cutoff. See for example the simulations (with David McBean's Horn Response Analysis program) in this diagram.

The size of the compression chamber depends on the drivers and the frequency range you want from the horn. For a rear-loaded bass driver such as in a Lowther horn, the front compression chamber volume tends to vary from about 2.5 liters to 4 or more liters.

 Vas: Ltr. lower Cut-Off frequency (fg): Hz fs Hz Throat area (Ah): m2     ( 300cm2 = 0.03m2 ) Qts Hz All fields are required!