## Throat Area I So Cm

1 PARABOLIC

2 CONICAL

3 EXPONENTIAL

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1 ooo FREQUENCY, Hz

1 ooo FREQUENCY, Hz oooo

The presence of a horn increases the impedance that is presented to the driver diaphragm. This causes the diaphragm to push against a higher pressure, which, although it makes the driver work harder, also allows more energy to be transmitted to the air. The resistive load placed on the diaphragm is almost totally dependent on the shape of the horn. Figure 6.27 plots the acoustical resistance of an infinitely long horn for five different shapes. As the diagram shows, a conical (straight-sided) horn does not add significant loading to the diaphragm. The cylindrical tube presents an even loading but has no increase in mouth area. The exponential horn, so called because the shape of its sides follows the exponential equation

where S = horn area at distance x (m2) S0 = throat area at x = 0 (m2) m = flare constant (m-1) x = distance from the throat (m) provides smooth loading down to a cutoff frequency fc = â€” (6.71)

c 4 n below which sound does not propagate without loss. Although the loading is constant with frequency for an exponential horn, the shape is not necessarily the best choice. For low-frequency directional control, the horn mouth size has to be relatively large, which leads to high-frequency control problems.

As we have seen from the piston in a baffle analysis, loudspeakers undergo a narrowing in their coverage pattern, called beaming, at high frequencies. To achieve wide coverage, high-frequency drivers must be physically small. Small drivers, however, are inefficient since they neither travel very far, nor push much air. Coupling a small driver to a horn helps solve both the beaming and the efficiency problems. Horn efficiencies as high as 50% can be achieved over a narrow range of frequencies; however, for broadband signals an efficiency of 10% is more likely. The sensitivity of a typical large format horn/driver is about 113 dB, which, with an on-axis Q of 20, represents an efficiency of a little more than 13% or an acoustic power of about 0.13 Watts.

At mid frequencies, where the size of the driver mouth is small with respect to the wavelength, the sound illuminates the side walls and allows them to control the directional pattern emanating from the horn. With constant directivity horns, the side walls are either straight or slightly curved, having different centers of expansion in the horizontal and vertical dimensions. This innovation was introduced by Paul Klipsch in 1951 and has been used in most subsequent horn designs. It allows for a different coverage angle in the horizontal and vertical planes.

### Constant-Directivity Horns

Constant-directivity horns are specifically designed to provide an even frequency distribution with direction. A typical example is shown in Fig. 6.28. In the ideal case, the sound spectrum measured at any particular location should be no different from that measured at any other location within the field of the horn's coverage. One result of this type of behavior is that the spectrum at any point is quite close to the actual power spectrum of the driver, since the power is evenly distributed. This feature is critical for successful sound system design and greatly simplifies the design process.

Modern constant directivity horn design started with the work of D. B. (Don) Keele, Jr., John Gilliom, and Ray Newman at Electrovoice in the middle of the 1970s. Their work introduced the features that are the central methods for controlling directivity in all current horn design. Their first design idea was a contraction in the throat immediately following

Figure 6.28 Constant Directivity Hornâ€”Nominal 60 x 40 (JBL 2365)

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